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Simple perfect squared squares of order 27
Citation for published version (APA):Bouwkamp, C. J. (1998). Simple perfect squared squares of order 27. (EUT report. WSK, Dept. of Mathematicsand Computing Science; Vol. 98-WSK-01). Technische Universiteit Eindhoven.
Document status and date:Published: 01/01/1998
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EINDHOVEN UNIVERSITY OF TECHNOLOGYDepartment of Mathematics and Computing Science
Simple Perfect Squared Squares of order 27
by
C.J. Bouwkamp
EDT Report 98-WSK-01Eindhoven, July 1998
Department of Mathematics and Computing Science
Eindhoven University of Technology
P.O. Box 513
5600 MB Eindhoven, The Netherlands
ISSN: 0167-9708
Coden: TEUEDE
Simple Perfect Squared Squares of order 27
C.J .Bouwkamp
Abstract
This report is a sequel to our Catalogue of Simple Perfect Squared Squares of
orders 21 through 25 and Album of Simple Perfect Squared Squares of order
26. It lists the 227 squares of order 27 known at present. They were obtained
by computer and/or transform technique. Two open questions are emphasized.
First, how can we get all possible order-27 squares, by computer, of course?
Secondly, has transform technique, other than empiricism and trial, a mathe
matical basis in properties of symmetry in electric network theory? For the first
we only need better computers, but solving the second problem is not that easy.
The author gives details of many transforms, their parametrization, clusters,
hoping that this may be of help in solving the second open problem.
1. Introduction
This report is a sequel to our Catalogue of Simple Perfect Squared Squares of
orders 21 through 25 and Album of Simple Perfect Squared Squares of order 26,
with 207 and 441 squares respectively. We recall that there are no other SPSS
of order less than 27. See references [1] and [2] for nomenclature, acronyms,
and the like.
Our knowledge about SPSS of orders greater than 26 is quite limited. At this
moment we have only 227 of order 27, but there might exist between one and
two thousand of them. The situation is even worse for order 28, with 234 known
squares, let alone order 29 with 226 and order 30 with 243 squares. This report
is devoted to squares of order 27.
There are two ways to discover SPSS of order 27. The older of them is by
transformation techniques due to PJF (Transforms I and II) and TRW (Trans
forms III, IV, V, VI and VIII). The newer is AJWD's computer approach
since 1978 when AJWD found the smallest-order SPSS, now on the cover of
J.Combinatorial Theory A, B. New transforms were discovered by JDSII and
CJB, while AJWD's computer approach was continued by JDSII aswell.
To end this introduction, I want to mention two open problems: (1) What is the
II
number of different SPSS of order 27, and (2) Ras transformation technique,
other than empiricism and trial, a mathematical basis in properties of symme
try of network theory. The first problem seems beyond'the power of today's
personal computers only, but the second problem is, I think, very difficult to
solve, if possible at all. Anyway, this report will introduce the reader into many
old and new transforms, clusters of two or more squares, and cluster member
ship of a square will be indicated if applicable. By so doing I hope to contribute
in a way to possibly solving problem (2).
2. A selection of transforms
Figure 1 shows transforms I (at left) and II (at right) due to JPF, and my own
variations la, Ib, and lIa, lIb, lIe. Especially lIe, recently discovered, is added
to the list in reference [2]. It first occurs in order-27 squares.
Figure 2 shows TRW's transform III and my own variant IlIa. Note that the
drawings are in conformity with our standard form of SPSS (element at top-left
is largest).
Figure 3 shows THW's IV and VI, followed by Figure 4 with THW's V and my
Va.
Figures 5 and 6 show TRW's VIII and my own VIlla, Vlllb, and Ville.
Transform VII of TRW is not reproduced, because we have as yet only one
example of it, and the square involved is trivially imperfect.
Figure 7 shows my own transform CJB-1, so named in Skinner's book [3], in
terms of new parameters A, Band C. Note that the octagon is just shifted
toward the left. Thus in the (electric) polar nets of the two squares, the dual
of this octagon's polar net does not occur.
Figure 8 shows CJB-4, in which the octagon rotates over a quarter turn.
Figure 9 shows CJB-5, where the hexagon is rotated and reflected.
The next four Figures (10, 11, 12, 13) show beautiful examples of a so-called
"castle-and-moat" transform, where the castle is rotated while the outer bound
of the moat is not changed. By the way, the terminology is Skinner's.
Finally, Figures 14 and 15 show transform CJB-28 and its variant CJB-28a.
In all these Figures, the letters A, B, C, ... and their combinations stand for
integers denoting the size of elemental squares. This parametrization is not
unique, sometimes not easy, because the number of parameters is always small
in comparison with the degree of freedom in drawing diagrams.
iii
A-C
B-C
I
A B
~~
A-C
B-C
II
A B
-C
A-C -
B-C
Ia
A B
I C I
A-C
B-C
lIa
A B
C
A B
,..---
ClIb
A-C
B-C
A B
ICIb
N:A+B-C N+l:A+BTRANSFORM I
A-C
'-- B-C
B-C
A-C
lIe
A B
-C
Figure 1
N:A+B-C N+l:A+BTRANSFORM II
IV
B
,C
A
C+2D
N:A+B+C+D
A+C+DA+B
A-D
..D
C+DA+D
N+l: 2A+B+C+D
TRANSFORM III
C
C+2D
A
D
B
N: A+B+C+D
A+C+D A+B
A-D
D
A+D C+D
N+l : 2A+B+C+D
TRANSFORM IlIa
Figure 2
A
r-------,C ID
B
N: A+B+C+D
v
A+D
D
C+D
B+D
N: A+B+C+2D
TRANSFORM IV
A B
A-C C~
B-C+DC-2D
N:A+B
A+D B+D
C-DB-C+2D
D_~
C+D A-C+D
N: A+B+2D
TRANSFORM VI
Figure 3
VI
B+C
TZ A-D
N: A+B+C
B+D
A-C D
N:A+B+D
TRANSFORM V
B+C
I---C A-D
N:A+B+C
B+D
A-C D
N:A+B+D
TRANSFORM Va
Figure 4
N: Cx2C
A
Vll
C
2C-A-B
C-A
C-B
N+2: 3C-A-B
TRANSFORM VIII
A
B
N: Cx2C
C
2C-A-B
C-A
I
C-B
N+2: 3C-A-B
TRANSFORM VIlla
Figure 5
viii
A
I B I
N: Cx2C
TRANSFORM VIIIb
2C-A-B
N+2: 3C-A-B
C
C-A
C-B
I--A- B+C
A+B+C-D A-C
B-C
BC+D
A+B-C
A+2B-2C
B-CA
A-2C A+B-D
2B-2CD
N : (A+B)x(2A+2B)
TRANSFORM VIlle
Figure 6
N+2 : 2A+3B-3C
A-2B+CA+B A+2B
B
A
C
A+C A+2C A+B-2C
N: 3A+B+C
A-B+C A+CA+3B
A+B+C
C
A+3C A+B-C A+B
N : 3A+2B+2C
TRANSFORM CJB-l
Figure 7
><"
20A-2B 2lA-2B
54A-6B19A-2B
22A-2B
4A/
26A-2B
20A-3B A+2B IB
2lA-B 22A+B 26A-6B 26A-4B
N : 95A-lOB
29A-2B 28A-4B
44A-4B A+2B
27A-6B
29A-3B 30A-3B
23A+B
1/ 4A B~
28A-3B 27A-3B 23A-3B 23A-B
N : lOlA-lOB
><
TRANSFORM CJB-4
Figure 8
29A-2B 28A-4B
44A-4B +2B
15A-2B27A-6B
29A-3B 30A-3B
23A+B
4A B~
28A-3B 27A-3B 23A-3B 23A-B
N : lOlA-lOB
41A-4B
69A-6B
20A-2B 21A-2B
19A-2B22A-2B
2IA-B 22A+B /4A26A-6B
15A-2B
20A-3B 'A+2B 2B 26A-2B15A
N+I : llOA-IOB
TRANSFORM CJB-5
Figure 9~.
2A-3B+2C\ 3C-7A+8B
d I A
5C-8A+9B I A-2BHC8A-7B-C I
es •...
4C-B
B
18A-19B-2C 5C-9A+l0BI , I 9A-8B-C
3C-6A+7B1
N : 24A- 24B+8C
TRANSFORM CJB-24
Figure 10
9A-l0B-CI
N : 24A-24B+8C
\A-4B+2C
\C-SA+7B
12A-12B+3C2A-3B+2C\
8A-7B-C
4C-B
B
N : 24A- 24B+8C
I
/10A-llB-C
SC-8A+9B
18A-19B-2C
12A-12B+C
12A-12B+SC
12A-12B+7C
A-2B+4C
9A-8B-C
AV3A-4B+2C
3C-7A+8B/
~9A-I0B-C17A-18B-2C 4C
SC-9A+lOB
N+l : 24A-24B+12C g:
TRANSFORM CJB-25
Figure 11
A
A-2B+4C
3C-7A+SB\
5C-9A+10BI i I
><:;:"
12A-12B+5C
12A-128+7C
5C-SA+9BlSA-19B-2C
10A-lIB-C--...,.
,....-.-,-,V3C-SA+78
2A-3B+2C,./'B
SA-78-G 4C
4C-B
9A-SB-C
12A-12B+C
\3A-48+2C
9A_I0B_C
'
17A-lS8-2C
12A-12B+3C
N : 24A..,... 24B+8C N+l : 24;A..,...24B+12C
TRANSFORM CJB-26
Figure 12
A-2B+4C9A-8B-C SC-8A+9B'18A_19B_2C
A
3C-7A+8B 3A-4B+2C
10A-llB-C"",
2A-3B+2C~ h-t'3C-SA+7B
B
7A-18B-2C!+-SC-9A +lOB
8A-7B-C4C-B
N+l : 24A-24B+12C N+l : 24A-24B+12C
TRANSFORM CJB-27
Figure 13
~
A A+B-E
B+C-D+E
C
N: A+B+C
A+B D
B
E A-C+D-E
N+l:A+B+D
><:::.
TRANSFORM CJB-28
Figure 14
A A+B-E
B+C-D+E
C
N: A+B+C
A+BD
B
A-C+D-EE
N+l:A+B+D
TRANSFORM CJB-28a
Figure 15><~:
XVlll
3. Clusters of squares
As in our Catalogue [1] and Album [2], the squares are ordered in the standard
way, here numbered from 1 to 227, as shown at bottom of page. Following lines
for Code and Elements, a third line may appear under the heading Remarks.
Since more than one third of the squares were discovered by transform tech
niques, it is worthwhile to give details by means of clusters as defined in [2].
Drawing all possible clusters and giving parameters is impossible, for lack of
space.
The first cluster occurs at number 8, a 3-cluster with two squares of order
26, namely A19 and A31, where A (now) refers to our Album [2]. See Figure
16 for transforms I, 4, and 5. Note that Remarks does not contain details of
parametrization. For transform I the parameter list is (A,B,C)=(201,119,45);
for (CJB-)4 and (CJB-)5, this is (A,B)=(3,1).
Also shown in Figure 16 is one of the many existing 4-clusters. It is very
special, because all four castle-and-moat transforms 24 through 27 are involved
in combination with two transforms 1. The four have parameters (A,B,C) =
(81,63,44) and the two have (524,436,176). See, then, Remarks for 178 and
179, where the details are omitted. In most 4-clusters the six transforms are
different and/or have more than three parameters.
Remarks about 5-clusters is even more condensed, in that the very 10 transforms
involved are not specified. Moreover, 6-clusters, with 15 transforms, are not
mentioned at all.
In Remarks a number may be preceded by A or C, where A refers to our Album
[2], and C refers to our volume of known SPSS of order 28 (unpublished).
Otherwise, a number refers to the present table.
Transform VIII and its variants, for 1x2 rectangles [5,6] and squares are included
aswell. They form 2-clusters, or just pairs.
Finally, if some square belongs to a 5-cluster, it does not mean that it is mem
ber of any 4-cluster. Membership is also temporal. The square could become
member of some 6-cluster if and when more squares of order 27 became known.
3-cluster
4-cluster
Figure 16
XIX
xx
4. References
[1] C.J .Bouwkamp and A.J.W.Duijvestijn, Catalogue of Simple Perfect Squar
ed Squares of orders 21 through 25, EUT Report 92-WSK-03, November
1992, Eindhoven University of Technology, Eindhoven, The Netherlands.
[2] C.J.Bouwkamp and A.J.W.Duijvestijn, Album of Simple Perfect Squared
Squares of order 26, EUT Report 94-WSK-02, December 1994, Eindhoven
University of Technology, Eindhoven, The Netherlands.
[3] Jasper Dale Skinner, II, Ph.D., Squared Squares Who's Who and What's
What, published by the author, 1740 North 59th Street Lincoln, Nebraska
68505, U.S.A., ISBN 0-9636569-0-2.
[4] C.J .Bouwkamp, On some new simple perfect squared squares, Discrete
Math. 106/107 (1992) 67-75.
[5] A.J.W.Duijvestijn, Simple perfect squared squares and 2x1 squared rect
angles of order 25, Math. Comput. 62 (1994) 325-332.
[6] A.J.W.Duijvestijn, Simple perfect squared squares and 2x1 squared rect
angles of order 26, Math. Comput. 65 (1994) 1359-1364.
[7] C.J .Bouwkamp, On step-2 transforms for simple perfect squared squares,
Discrete Math. 179 (1998) 243-252.
Eindhoven, June 1998.
Acknowledgments
Thanks are due to Herman Willemsen for producing the originals of all figures
plus text thus far, and to Fred Simons for the originals of all squares and
comments that follow.
Order 27, reduced side 218
62
81 75
13
6 1249f-~
20 24 3031 18 46
165 10
3326 21 43
3927 29
8070 68
AJWD
Code: (81,75,62)(13,49)(12,30,46)(31,20,24,6)(18)(16,4)(33, 43)(10,39)(26,5)(21)(27,29)(80)(70)(68)
Elements: 4,5,6, 10, 12, 13, 16, 18,20,21,24,26,27,29,30,31,33, 39,43,46,49,62,68,70,75,80,81
Order 27, reduced side 254
131123
8
27 20 2319
'7T9li 45
52 18 [16 2268 33
15
2913
8671
5542
JDSII
Code: (131, 123) (8, 27, 20, 23,45) (68, 52, 19) (7, 9, 4) (1, 22) (5) (33, 18,2) (16) (15,86)(29,71)(55,13)(42)
Elements: 1,2,4,5, 7,8,9, 13, 15, 16, 18, 19,20,22,23,27,29,33, 42,45,52,55,68, 71,86, 123, 131
2
Order 27, reduced side 277
129148
2533
23 1817 I9 71
56 3269
49 6
14 13 26
2915 21 18
77
60 5744 39
JDSII
Code: (148, 129)(25,33,71)(56,69,23)(17,8)(9,32)(49)(26,6)(77) (29,14,13)(1,60,21)(15)(18,57)(44)(39)
Elements: 1,6,8,9,13,14,15,17,18,21,23,25,26,29,32, 33,39,44,49,56,57,60,69,71, 77, 129, 148
3
Order 27, reduced side 300
7895
127
17
32 6141 39
36 16 18 19 1449 27
74 4713 34 33
25 5037
11499
87
AJWD
Code: (127,95,78) (17, 61) (32, 41,39) (74, 49, 36) (2,18,19) (27,16) (14,47) (34) (33)(13,50)(25,37)(114)(99)(87)
Elements: 2, 13, 14, 16, 17, 18, 19,25,27,32,33,34,36,37,39,41,47, 49,50,61, 74, 78,87,95,99, 114, 127
4
Order 27, reduced side 303
8796
120
44 43 2234
G2C40
1130 8
1936 37
79 54 48
49 17
56
24
119104
80
AJWD
Code: (120,87,96)(44,43)(34,22,40)(12,10)(79,30, 11)(2, 8)(37,54)(19,36)(48)(49)(56,17)(119)(104,24)(80)
Elements: 2,8, 10, 11, 12, 17, 19,22,24,30,34,36,37,40,43,44,48, 49,54,56,79,80,87,96,104,119,120
5
Order 27, reduced side 305
99 97109
2616 43
52
7542 9
93 34
761
35
5363
2522
r-- 39
17
103
7868
56
JDSII
Code: (109,99,97) (2, 43,52) (26, 75) (93, 16) (42) (34, 9) (61) (35,7) (53,63) (103, 25)(22,39)(78)(5,17)(68)(56)
Elements: 2,5, 7, 9, 16, 17,22,25,26,34,35,39,42,43,52,53,56, 61,63,68,75,78,93,97,99, 103, 109
6
Order 27, reduced side 318
139
179
40
99
47 52 48
72
~~ 1838 13 17
31 ~ 3012 19
16 14 11
8067 6154 56
AJWD
Code: (179,139) (40, 99) (47,52,72,48) (38, 9) (18, 30) (4,17,31) (13) (19,80) (6,12)(16, 14) (11, 67) (61) (56) (54)
Elements: 4,6,9,11,12,13,14,16,17,18, 19,30,31,38,40,47,48,52,54,56,61,67,72,80,99,139,179
7
Order 27, reduced side 320
119
201
58 61
5564
62 67 72 12
43
20 762357 52 I13TI
~47 45
19 24
Code: (201,119) (58, 61) (55,3) (64) (62, 67, 72) (43,12) (76) (57, 5) (52,20) (23, 47, 2)(45)(13,7)(6,1)(24)(19)
EleDlents: 1,2,3,5,6,7,12,13, 19,20,23,24,43,45,47,52,55,57,58,61,62,64,67,72,76, 119,201
ReDlarks: In cluster with A19, A31. TransfofDls I, CJB-4, CJB-5.
8
CJB
Order 27, reduced side 328
94105
129
425234
71
47 2937
82 ~.l.L- 62
35 31 32 2561
30
117 120
91
AJWD
Code: (129, 105,94) (42,52) (71, 34) (82, 47) (3, 29, 10) (37) (62) (11, 18) (35, 61, 31,32,7)(25)(30,1)(120)(117)(91)
Elements: 1,3,7,10,11,18,25,29,30,31,32,34,35,37,42,47,52, 61,62,71,82,91,94,105, 117, 120, 129
9
Order 27, reduced side 328
151
177
6982
4759
71
1~ 21 I11 13
'9 I 7 16 56i-'-'---30 44
23
9580
53 48 52
Code: (177,151)(69,82)(71,47,59)(56,13)(15,21,11)(95)(10, 1) (16,44)(9,6)(30,7)(80)(23) (53)(4,52)(48)
Elements: 1,4,6,7,9,10,11,13,15, 16,21,23,30,44,47,48,52,53,56,59,69,71,80,82,95,151,177
Remarks: In cluster with A20, A22. Transforms I, Ib, IV.
10
CJB
Order 27, reduced side 336
135
201
6273
34 51 3152 4768 53
21 13 922
~
16 3233 24
17
8867 75
50 56
Code: (201, 135) (62, 73) (51, 11) (68, 52, 34,47) (31, 53) (21, 13) (9, 22) (32,88) (16,33,3)(24)(75)(67,17)(56)(50)
Elements: 3,9,11,13,16, 17,21,22,24,31,32,33,34,47,50,51,52, 53,56,62,67,68,73,75,88,135,201
Remarks: In cluster with A8. Transform II.
11
CJB
Order 27, reduced side 341
165176
24 3141 r--
47 17 7 695772 38
25 I2213 58
~
44 ~ 1920
10793
7764
Code: (176,165) (41, 24, 31, 69) (57, 72, 47) (17, 7) (38) (58) (25, 22) (44,13) (107) (3,19)(11,2)(9,93)(20)(77)(64)
Elements: 2,3,7,9,11,13,17,19,20,22,24,25,31,38,41,44,47, 57,58,64,69,72,77,93,107,165,176
Remarks: In cluster with A9. Transform I.
12
CJB
Order 27, reduced side 350
160
190
44 40
15 76
53 51 16 17\ 363071 13120
18 4135 37 34
114
8972 75
JDSII
Code: (190,160)(44,40,76)(71,53,51, 15)(4,36)(1,17,30)(16)(20,13)(41,2)(114)(37,34)(18,35)(89)(75)(72)
Elements: 1,2,4,13,15,16,17,18,20,30,34,35,36,37,40,41,44, 51,53,71,72,75,76,89, 114, 160, 190
13
Order 27, reduced side 364
163
201
64
9946
7283 29 35
9
37
18 I 38 32
43-----lL
25 44102
20 80 7048
f--- 8
28 36
JDSII
Code: (201,163)(64,99)(72,83,46) (29,35)(37,9)(38)(32,102)(43,18,11)(7,44,80)(25)(70)(48,20)(8,36)(28)
Elements: 7,8,9,11, 18,20,25,28,29,32,35,36,37,38,43,44,46,48,64, 70, 72,80,83,99,102,163,201
14
Order 27, reduced side 375
94119
162
25
6944
26100
2850 58 57 56
24 30
74 6679
16 15635 -
19
8976
54
AJWD
Code: (162,94,119) (69,25) (44,100) (50, 26, 28, 58) (57, 56) (24, 2) (30) (74) (156) (66,79)(89,35,16)(3,76)(19)(54)
Elements: 2,3,16,19,24,25,26,28,30,35,44,50,54,56,57,58,66, 69,74,76,79,89,94,100, 119, 156, 162
15
Order 27, reduced side 378
93 104
181
82
115
22l20J 33 32 38 44
7417-r4131
35 41
69
27
159
123
96
AJWD
Code: (181,93,104)(82,11)(115)(38,44)(74,22,20,33,32)(7, 13) (17,5)(12)(1,69)(6,41)(159)(35)(123,27)(96)
Elements: 1,5,6,7,11,12,13,17,20,22,27,32,33,35,38,41,44, 69,74,82,93,96,104,115,123,159,181
16
Order 27, reduced side 381
109 103
169
41
6049 62
20 21
32 I 26
6483
89 8758
25 ~~ 23 8
123 125 133
AJWD
Code: (169,109,103) (41, 62) (60, 49) (20, 21) (11, 32, 6) (26) (83) (89, 64,87) (58) (25,16,23) (8, 133) (9, 7) (125) (123)
Elements: 6, 7, 8, 9,11, 16,20,21,23,25,26,32,41,49,58,60,62, 64,83,87,89, 103, 109,123, 125, 133, 169
Remarks: In cluster with ClO. Transform I.
17
Order 27, reduced side 384
173
211
7796
5568
88 1913
20 ~1~ 2258
25 42
-29 27 28 24
115
85 7656 52
Code: (211, 173) (77, 96) (88, 68, 55) (58, 19) (13, 42) (115) (20, 14,22, 25) (6,8) (85,29)(27,3)(28)(24,76)(56)(52)
Elements: 3,6,8,13,14, 19,20,22,24,25,27,28,29,42,52,55,56,58,68, 76, 77,85,88,96, 115, 173, 211
Remarks: In cluster with A38. Transform 1.
18
CJB
Order 27, reduced side 386
185201
16
6853 59 101
105
24 35 3347 41 f------t-,
17r32 34
25 30
10080 85
5566
. AJWD
Code: (201, 185)(16,68, 101)(105,53,59)(35,33)(47,6)(41,24)(17,7)(34,100)(3,32)(10)(30,85)(80,25)(66)(55)
Elements: 3,6,7,10,16, 17,24,25,30,32,33,34,35,41,47,53,55, 59,66,68,80,85,100,101,105,185,201
19
Order 27, reduced side 391
103
134154
31
72
33 7147 94
~ 74 3042
~ 29 27 23
66 5453 55
163
108120
AJWD
Code: (154, 134, 103) (31, 72) (94, 71) (33, 47, 74) (30, 42) (19, 14) (5, 29,27) (23, 66,12)(24)(54)(55,163)(53)(120)(108)
Elements: 5,12,14,19,23,24,27,29,30,31,33,42,47,53,54,55,66, 71,72,74,94,103,108, 120, 134, 154, 163
Remarks: In cluster with C16. Transform 1.
20
Order 27, reduced side 391
172
219
43 5376
31 3347
73 68 22Zk 63
t-- 20 4026 21 15 58
27
99 104 10385
Code: (219,172) (76, 43, 53) (33,10) (73, 47,68,31) (63) (11, 58,40) (22,9) (20) (26,21)(15,7)(27)(104)(103)(99)(85)
Elements: 7,9,10,11,15,20,21,22,26,27,31,33,40,43,47,53,58, 63,68,73,76,85,99,103, 104, 172,2] 9
Remarks: In cluster with A30. Transform II.
21
CJB
Order 27, reduced side 403
186
217
79
48 107
7594
2846 53
24 2551 Pm 36
16110
92 8560 56
AJWD
Code: (217,186)(79, 107)(75,94,48)(46,53,28)(51,24)(25, 110)(5,36,92,7)(14,15)(85)(13,1)(16)(60,4)(56)
Elements: 1,4,5,7,13,14,15,16,24;25,28,36,46,48,51,53,56,60, 75, 79,85,92,94,107,110,186,217
22
Order 27, reduced side 405
107
141157
34
73
5139
8569
88
63100
2945
2680 25
6236 35 67
16
12598 99
83
AJWD
Code: (157, 141, 107) (34, 73) (85, 51, 39) (88, 69) (12, 100) (63) (45,80, 29) (62, 26)(67,25)(36,35)(125)(99,16)(98)(83)
Elements: 12,16,25,26,29,34,35,36,39,45,51,62,63,67,69, 73,80,83,85,88,98,99,100, 107, 125, 141, 157
23
Order 27, reduced side 406
195211
61 52
58 59 82
94 ~ 3020
32 r;- 4622 2136
4329
129101 104
72
AJWD
Code: (211,195)(61,52,82)(94,58,59)(9, 13,30)(20,46,4)(17)(36,22)(21,32,6)(26)(129)(43)(104)(101,29)(72)
Elements: 4,6,9, 13, 17,20,21,22,26,29,30,32,36,43,46,52,58, 59,61,72,82,94,101,104,129,195,211
24
Order 27, reduced side 407
102
131
174
29
73
51
201
19 18 10936
16f" 4B30 58
99
63
78
28
167
134
106
AJWD
Code: (174,102,131)(73,29)(51,109)(99,36,20, 19)(18,48,7)(58) (1,6,30)(16,5)(11)(63)(78)(167)(134,28)(106)
Elements: 1,5,6,7,11,16,18,19,20,28,29,30,36,48,51,58,63, 73,78,99,102,106,109,131,134,167,174
Remarks: In cluster with C11. Transform 1.
25
Order 27, reduced side 410
191219
4056
19
~13395
17101 99 39
22
5432
1-'--37
24 43124
90 92
55 49
JDSn
Code: (219,191) (40, 56, 95) (101, 99,19) (7, 33) (26) (17, 39) (54, 22) (32,124) (13, 37,43,92)(90,11)(24)(55,6)(49)
Elements: 6,7,11,13,17, 19,22,24,26,32,33,37,39,40,43,49,54, 55,56,90,92,95,99,101,124,191,219
26
Order 27, reduced side 414
111131
172
4368
4818 25
83
37 29
82 RT:'":L75 ~108
38 31
8026
40
160134
120
AJWD
Code: (172, 111, 131) (43, 68) (48,83) (18, 25) (108, 82) (75,37,29) (8, 15,6) (9,80)(38,7)(31)(26,160,40)(134)(120)
Elements: 6,7,8,9,15,18,25,26,29,31,37,38,40,43,48,68,75, 80,82,83,108,111,120,131,134,160,172
27
Order 27, reduced side 416
115
156 145
30
85
44 55
112120
4673 65
27 19
4345 53
64 60
21 22
151
8498
83
AJWD
Code: (156, 115, 145)(85,30) (55, 120)(112,44)(73,46,65) (27, 19) (53, 151) (64, 43,5)(60,45)(21,22)(98)(84,1)(83)
Elements: 1,5, 19,21,22,27,30,43,44,45,46,53,55,60,64,65, 73, 83,84,85,98, 112,115,120,145,151,156
28
Order 27, reduced side 417
130 137150
6585 123
144
25'--- 40
3015
27 29 2880
6445
3656
23
136
102 10079
AJWD
Code: (150,130, 137)(123, 7)(144)(85,65)(25,40)(80,5)(30)(2,29,64,28)(15,27)(45)(36,136)(56)(102,23)(100)(79)
Elements: 2,5, 7, 15,23,25,27,28,29,30,36,40,45,56,64,65, 79, 80,85, 100, 102, 123,130,136,137,144,150
29
Order 27, reduced side 419
194
225
4762
85
59 54 11532 117
112 6043
64
14030 19 1~ 29I 103
82
52 42
Code: (225,194)(85,47,62)(112,59,54)(32, 15)(17,60)(6,43)(5,140)(64)(103)(82,30)(19,16,29)(3,13)(52)(42)
Elements: 3,5,6,13,15,16,17, 19,29,30,32,42,43,47,52,54,59,60,62,64,82,85,103,112, 140, 194,225
Remarks: In cluster with A43. Transform II.
30
CJB
Order 27, reduced side 431
107
138
186
4067 9
49H2922
129
7352 71
106
33 44 4836
164139
128
JDSII
Code: (186,107,138) (67, 40) (9,129) (49) (16, 29,22) (106, 73, 7) (3, 13) (10) (71) (52)(4,48)(33,44)(36,164)(139)(128)
Elements: 3,4, 7, 9, 10, 13, 16,22,29,33,36,40,44,48,49,52,67, 71, 73, 106, 107, 128,129, 138, 139, 164, 186
31
Order 27, reduced side 432
109
167 156
39
70
31 1 23
67
100141
12433 34
36 35
96
72
13512927
1569
5742
JDSII
Code: (167, 109, 156) (70,39) (31, 8) (23, 141) (l00, 67) (124) (33,34) (96,36, 1) (35)(6,135)(72,129)(69,27)(15,57)(42)
Elements: 1,6,8,15,23,27,31,33,34,35,36,39,42,57,67,69, 70,72,96,100,109,124,129,135,141,156,167
Remarks: In cluster with 33, C24, C26, C28.
32
Order 27, reduced side 433
109
168 156
39
701111
23 1 31
4269 57
27 15141
124
72
96
36 35
33 34
136 130100
67
Code: (168, 156, 109) (39, 70) (8,31) (141, 23) (69, 42, 57) (124) (27, 15) (72) (96) (36,35,136,6)(130)(1,34)(100,33)(67)
Elements: 1,6,8,15,23,27,31,33,34,35,36,39,42,57,67,69, 70,72,96,100,109,124,130, 136, 141, 156, 168
Remarks: In cluster with 32, C24, C26, C28.
33
CJB
Order 27, reduced side 439
183
256
90 93
70 75 32 2958 64111
26 35
65 56
39 108 9972 21
33 r~ 48 52
Code: (256,183) (90, 93) (111, 70,75) (58, 32) (29,64) (26, 35) (65, 5) (56, 108) (99) (72,39)(4,52)(21,48)(33,6)(27)
Elements: 4,5,6,21,26,27,29,32,33,35,39,48,52,56,58,64,65, 70,72,75,90,93,99,108, 111, 183,256
Remarks: In cluster with A54. Transform II.
34
CJB
Order 27, reduced side 443
211232
97114
100
132
21 Hir----'--""
5736
52 48
33 120 15
I118
79 7859 63
46
PJFffHW
Code: (232,211)(97,114)(132,100)(57,21, 10,9)(1,8)(11)(4, 118) (36)(52,48)(79,33,20)(15,78)(63)(13,59)(46)
Elements: 1,4,8,9,10,11,13,15,20,21,33,36,46,48,52,57,59,63, 78, 79,97,100,114,118, 132,211,232
Remarks: In cluster with 42, A75, A86. Transforms I, Ib, II, III, N, V.
35
Order 27, reduced side 447
126 123
198
52 556874
57 61 948178 76
~~ 34
1743
48 53
171 175
101
Code: (198,126, 123) (55, 68) (74, 52) (94, 13) (81) (57, 61, 78, 2) (76) (43, 14) (10, 34,17) (24) (175) (171) (5, 53) (48) (101)
Elements: 2,5,10,13,14,17,24,34,43,48,52,53,55,57,61,68,74, 76,78,81,94,101,123,126, 171, 175, 198
Remarks: In cluster with C33. Transform II.
36
CJB
Order 27, reduced side 452
203
249
80
123
6276
111 37 43
~53
39 46 4017 20
32 I 28126
92 88 8660
AJWD
Code: (249,203)(80,123)(111,76,62)(37,43)(53,9)(46) (18, 19,39) (40, 126)(17, 1)(20)(92,32,4)(28,88)(86)(60)
Elements: 1,4,9,17,18, 19,20,28,32,37,39,40,43,46,53,60,62, 76,80,86,88,92,111,123,126,203,249
37
Order 27, reduced side 453
216237
2844 90
73 017 1269224
4819 36
5435 78
51
124 11189
69 60
AJWD
Code: (237,216)(90,126)(73,92,44,28)(11,17)(5,6)(48,1)(24) (78,36)(54,19)(35,124)(51,111)(89)(69,9)(60)
Elements: 1,5,6,9,11,17,19,24,28,35,36,44,48,51,54,60,69, 73,78,89,90,92,111,124,126,216,237
38
Order 27, reduced side 453
201
252
84
117
6388
101 24
t"9r 6025
38 32 27 ~61
2942
16113
100 108
7458
Code: (252,201)(117,84)(88,63, 101)(24,60)(9, 15)(25,38)(32,61,27,6)(21)(113)(108)(3,29)(100,42)(16,74)(58)
Elements: 3,6,9,15, 16,21,24,25,27,29,32,38,42,58,60,61,63, 74,84,88,100,101,108,113,117,201,252
Remarks: In cluster with A58. Transform II.
39
CJB
Order 27, reduced side 456
128145
183
17
73 11189
6923
114 18 E 5029
6045 42 34 8226
53
159 162135
JDSII
Code: (183, 145, 128) (17, 111) (89, 73) (114, 69) (23, 50) (18, 60, 11) (29,82) (4, 19)(15)(45,42)(34)(26,53)(162)(159)(135)
Elements: 4,11,15,17,18,19,23,26,29,34,42,45,50,53,60,69, 73,82,89,111,114,128,135, 145, 159, 162, 183
40
Order 27, reduced side 456
219237
68 56
60 66 95
17111
27 r2239
3624
54 48 f--
~2841
142108 105 101
·AJWD
Code: (237,219)(68,56,95)(111,60,66)(17,39)(36,27,5)(22) (54,6)(48,24)(41,142) (4, 32) (28) (108, 3) (105) (101)
Elements: 3,4,5,6, 17,22,24,27,28,32,36,39,41,48,54,56,60,66,68,95, 101, 105,108,111,142,219,237
41
Order 27, reduced side 458
211
247
9746 114
59 6379
I33 120 fH 21
52 48 r---57
36
132 133
100 93
PJFffHW
Code: (247,211)(114,97)(79,46,59,63)(33,13)(20,52)(9, 10,21,57)(48,15)(8,1)(11) (133, 4) (132) (36) (100) (93)
Elements: 1,4,8,9,10, 11,13, 15,20,21,33,36,46,48,52,57,59, 63,79,93,97, 100, 114,132, 133,211,247
Remarks: In cluster with 35, A75, A86. Transforms I, Ib, II, III, IV, V.
42
Order 27, reduced side 465
240225
54
57 7794
81J102 ffsi 40
33 22 16 17
21 604351 42
146123
93 103
. JDSII
Code: (240,225) (54, 94,77) (102, 81, 57) (14, 40) (4,10) (33,22,6) (17,60) (16) (146,43) (21, 51,9) (42) (123) (103) (93)
Elements: 4,6,9,10,14,16,17,21,22,33,40,42,43,51,54,57,60, 77,81,93,94,102,103,123,146,225,240
43
Order 27, reduced side 465
223242
97126
119 123
29
68
r-;~ 37
3928
47~0125
104 116
63 n53 52
JDSII
Code: (242,223)(97,126)(119,123)(68,29)(39,116)(104,15)(11,37, 47,28)(26)(5,25,77)(13,20)(63)(6,7)(53)(52)
Elements: 5,6,7,11,13,15,20,25,26,28,29,37,39,47,52,53,63, 68,77,97,104,116,119,123,126,223,242
Remarks: In cluster with 56, An. Transforms lb, II, V.
44
Order 27, reduced side 467
117
154
196
25
rT-L 92
4429
106
64 62
132 103
5268
112
61
17155
139
9578
AJWD
Code: (196,154,117)(25,92)(12,13)(106,44, 15, 1)(14)(29)(132,64) (62,11)(103)(68,112,52)(155)(139,61)(17,95)(78)
Elements: 1, 11, 12, 13, 14, 15, 17,25,29,44,52,61,62,64,68, 78, 92, 95, 103, 106, 112,117, 132, 139, 154, 155,196
Remarks: In cluster with C30. Transfonn 1.
45
Order 27, reduced side 467
218249
37 904457 128
I20F J 11124 1 34
5238
8058
25 3145
107 121
81 82 76
AJWD
Code: (249,218)(90,128)(57,37,44,111)(20,17)(10,34)(3,24)(80) (52,38)(58)(45,121)(25,107,31)(1,82)(81)(76)
Elements: 1,3, 10, 17,20,24,25,31,34,37,38,44,45,52,57,58,76, 80,81,82,90,107,111,121,128,218,249
46
Order 27, reduced side 469
124
85
39
46
260
60
53
96 91
36
77
51
54
50
52
209
158
102
JDSII
Code: (260,209) (51, 158) (124, 96, 91) (41, 34, 16) (60, 36) (22, 50, 102) (85,39) (30,4)(26)(77)(54,2)(7,53)(52)(46)
Elements: 2,4, 7, 16,22,26,30,34,36,39,41,46,50,51,52,53,54, 60,77,85,91, 96,102,124,158,209,260
47
Order 27, reduced side 473
225248
56 66
62 10380 l::l~106 16 20
18 25 6144 3624
5731
145119 121
88
CJB
Code: (248,225)(103,56,66)(106,62,80)(22, 19, 15)(5,61)(20)(3,16)(25)(44,18)(36) (57, 145,24) (121) (119, 31) (88)
Elemen~: 3,5,15,16,18, 19,20,22,24,25,31,36,44,56,57,61,62,66,80,88,103,106,119,121,145,225,248
Remarks: In cluster with A61. Transform II.
48
Order 27, reduced side 483
199
284
105 94
2575 27 --C 69
102 107 t*78 31
2352
20
12197 92 101
72
PJFITHW
Code: (284, 199) (105,94) (102, 107,75) (25, 69) (78,27) (13, 12) (1, 11) (31, 10) (21)(52,23)(121)(101)(97,5)(92,20)(72)
Elements: 1,5,10,11,12,13,20,21,23,25,27,31,52,69,72, 75,78,92,94,97,101,102,105,107,121,199,284
Remarks: In cluster with A87. Transform 1.
49
Order 27, reduced side 484
227257
106 12189 76
92
41 48 39
~7122r.-- 69
27 I 33 151136
68 63 66
AJWD
Code: (257,227)(106,121)(89,92,76)(16, 151, 15)(41,48)(136)(39,69)(29,12)(6,33)(5,22,27)(17)(68)(3,66)(63)
Elements: 3,5,6,12,15,16,17,22,27,29,33,39,41,48,63,66,68, 69,76,89,92,106,121,136,151,227,257
50
Order 27, reduced side 490
246 244
51 ~73 36
99116 '--- 115
46 41
43 ~3:2317
I--~
44 40
147131128
84
AJWD
Code: (246,244) (8, 22, 99, 115) (116, 73,51,6) (14) (36) (46,5) (41) (43,30) (23,147,16)(13,17)(131)(128,44)(40)(84)
Elements: 5,6,8, 13, 14, 16, 17,22,23,30,36,40,41,43,44,46,51, 73,84,99, 115, 116,128,131,147,244,246
51
Order 27, reduced side 490
226
264
92
72 13481
111
39 l:- 50 4223
5827 35 38 46
41 t-T2°1
115130
74 87 84
AJWD
Code: (264, 226) (92, 134) (111, 72, 81) (50, 42) (39, 33) (58, 23) (46, 130) (35, 38) (6,27)(115,41)(20,7)(13,87)(84)(74)
Elements: 6,7,13,20,23,27,33,35,38,39,41,42,46,50,58,72,74, 81,84,87,92,111,115,130,134,226,264
52
Order 27, reduced side 491
215
276
61
15449 59 68 73
88
39
42 126 21
69I 52
31 3218
4025
127 122
87 9065
AJWD
Code: (276, 215) (61, 154) (88, 49, 59, 68, 73) (39, 10) (69) (42, 26) (21, 52) (127) (32,122)(16,31)(18,40)(25,90)(87)(65)
Elements: 10,16, 18,21,25,26,31,32,39,40,42,49,52,59,61,65, 68,69,73,87,88,90,122,127,154,215,276
53
Order 27, reduced side 492
238254
104134
123 131
30
74
3244
115 107 33 41 120
~76
22 17 35
Code: (254,238)(104,134)(123,131)(74,30)(44, 120)(115,8)(107,32) (1,41,76)(33) (20, 13) (6,35) (7,12) (22, 5) (17)
Elements: 1,5,6, 7, 8, 12, 13, 17,20,22,30,32,33,35,41,44, 74, 76, 104, 107, 115, 120,123,131,134,238,254
Remarks: In cluster with 64, A108. Transforms lb, II, V.
54
CJB
Order 27, reduced side 492
224
268
4459
34 12119
75 4087
116 53 §2226
1749 -----, '--23 20
137 147
108 100
AJWD
Code: (268,224) (44, 59,121) (116, 75, 87, 34) (19, 40) (53) (18, 22) (14, 4) (49, 26) (147)(17,137)(23,3)(20)(108,8)(100)
Elements: 3,4, 8, 14, 17, 18, 19,20,22,23,26, 34,40,44,49,53,59, 75, 87, 100, 108, 116,121,137,147,224,268
55
Order 27, reduced side 495
223
272
97126
63 53 52
104~OJ 25
~~ 37
2947
28 6839
146119 123
107
Code: (272,223) (126, 97) (104, 63, 53, 52) (29, 68) (7,20, 25) (47, 6) (13) (26,37) (28,5) (146, 39) (15, 11) (123) (119) (107)
Elements: 5,6,7,11,13, 15,20,25,26,28,29,37,39,47,52,53,63,68,97,104, 107,119,123,126,146,223,272
Remarks: In cluster with 44, A92. Transforms lb, II, V.
56
CJB
Order 27, reduced side 496
232264
108124
133 131
92
36 38 49 42140
99122~
63 -- 645237 41
Code: (264,232)(108,124)(133, 131)(92, 16)(140)(2,38,49,42)(99,36)(5,23,64)(63,11)(7,22,18)(52,15)(41)(37)
Elements: 2,5, 7, 11, 15, 16, 18,22,23,36,37,38,41,42,49,52,63, 64,92,99, 108, 124,131,133,140,232,264
Remarks: In cluster with Al15. Transform lb.
57
CJB
Order 27, reduced side 503
239264
25
105 10972
114 103
31 ~8J.::,- 32 2858
4381
60
125 136101
67 14
AJWD
Code: (264,239) (25, 105, 109) (114, 103, 72) (31, 18,23) (15, 58,32) (28, 81) (13,5)(43) (11, 136) (60) (125) (101) (7, 74) (67)
Elements: 5,7,11,13,15,18,23,25,28,31,32,43,58,60,67,72,74, 81,101,103,105,109,114,125,136,239,264
58
Order 27, reduced side 508
154140
214
60
108 126
39 5067 I--
118 28
I 374161 63
51 4422 93
56
176 183149
JDSII
Code: (214,154,140)(14,126)(60,108)(118,67,39, 50)(28, 11)(63,41,4) (61)(37,93)(51,44)(22,56)(7,183)(176)(149)
Elements: 4,7,11,14,22,28,37,39,41,44,50,51,56,60,61,63,67, 93,108,118,126,140,149,154,176,183,214
59
Order 27, reduced side 515
244271
: 2761
34
156127 137
95
39 38 5148
123 24117 115107
59 53 64
Code: (271,244)(27,61, 156)(127, 137,34)(95)(117,10)(8,39,38,51,115)(107,48)(1,24,13)(17,23)(64)(59,6)(53)
Elements: 1,6,8,10,13, 17,23,24,27,34,38,39,48,51,53,59,61,64,95,107, 115, 117,127,137,156,244,271
Remarks: In cluster with SPSR 25:244x488. Transform VIlla.
60
CJB
Order 27, reduced side 520
226
294
96130
61 66 77 90 3462
~1 I I56 5129 38 ~25
164136
109 111
AJWD
Code: (294,226)(96,130)(61,66, 77,90)(62,34)(56,5)(164)(51,20) (9,38,17,13)(29)(4,25,136)(21)(2,111)(109)
Elements: 2,4; 5,9,13,17,20,21,25,29,34,38,51,56,61, 62, 66, 77,90,96,109,111,130,136,164,226,294
61
Order 27, reduced side 521
249272
41 l:- 69104 29
77 81 47 ~114 24
7440 37 33 55
43 46
168135 129
89
Code: (272,249)(104,41,35,69)(77, 114,81)(6,29)(47)(24,5)(74) (16,55)(40,37)(33,168)(3,46,135)(43)(129)(89)
Elements: 3,5,6, 16,24,29,33,35,37,40,41,43,46,47,55,69, 74, 77,81,89, 104, 114,129,135,168,249,272
Remarks: In cluster with A94. Transform II.
62
CJB
Order 27, reduced side 524
142163
219
5231
905676
45 38
145 130121 128
36 2579
~6j 3560
160 164
96 104
cm
Code: (219, 163, 142) (52,90) (56, 76, 31) (45,38) (145, 130) (128) (121) (15, 79, 36)(25,60,164)(160)(26,35)(17,9)(104)(96)
Elements: 9,15,17,25,26,31,35,36,38,45,52,56,60,76, 79,90,96,104,121,128,130,142,145,160,163,164,219
Remarks: In cluster with C53. Transform 1.
63
Order 27, reduced side 534
238
296
104
W-==-134
20
115 107 33 41 30
7432 44
162
123 131 118
Code: (296,238) (134,104) (115,107,22,17,35) (5,12) (20,7) (13, 6) (41) (33) (30, 74)(32,1) (162, 44) (8,131) (123) (118)
Elements: 1,5,6,7,8, 12, 13, 17,20,22,30,32,33,35,41,44,74, 104,107, 115, 118, 123,131,134,162,238,296
Remarks: In cluster with 54, A108. Transforms Ib, II, V.
64
CJB
Order 27, reduced side 556
283 273
128145139 144
26 I44 41 1 24
46281=~ 4219
134 129 138
83 72
JDSII
Code: (283,273)(128,145)(139,144)(26,44,41, 17)(24, 138)(134,5) (129,46)(23,42)(28, 16) (12, 4)(8, 19)(83, 11)(72)
Elements: 4,5,8,11,12,16,17,19,23,24,26,28,41,42,44,46,72, 83,128,129,134,138,139,144,145,273,283
Remarks: In cluster with 70. Transform V.
65
Order 27, reduced side 557
156
203 198
6096
49
78
154 59 44 42180
I 31 3328 I
46 ~ 85
40 52
200178 179
AJWD
Code: (203,156,198)(96,60)(18,180)(154,49)(78)(59,44, 42)(2, 33,85)(15,31)(46,28)(12,52)(40)(200)(1,179)(178)
Elements: 1,2,12,15,18,28,31,33,40,42,44,46,49,52,59,60,78, 85,96,154,156,178,179,180,198,200,203
66
Order 27, reduced side 559
143161
255
125
179
57 66 5372
132
48 I 3919
7027 ~H31
51
219
172 168
AJWD
Code: (255,143,161)(125, 18)(179)(132,57,66)(53,72)(48,9)(39,70,19)(51,219)(27,14, 15,31) (13,1) (16) (172) (168)
Elements: 1,9,13,14,15,16,18,19,27,31,39,48,51,53,57,66,70, 72,125,132,143,161,168,172,179,219,255
67
Order 27, reduced side 566
138
191
237
5385
3263
30
73 r--- 149
4350 117
134
47 ~22 3661
I
6481
226195
145
AJWD
Code: (237, 191, 138) (53, 85) (63,149,32) (117) (134, 73, 30) (13, 50) (43) (14, 36) (61,47,8)(22)(17,81,226)(64)(195)(145)
Elements: 8, 13, 14, 17,22,30,32,36,43,47,50,53,61,63,64, 73, 81, 85, 117, 134, 138,145,149,191,195,226,237
68
Order 27, reduced side 574
170196 208
57
I 11339 120
56
59184 162
~454
11529 23
61
194 204176
JDSII
Code: (196,208,170) (57, 113) (184,12) (162,39,19) (20,56) (59) (54, 115) (35, 24)(17,7)(61)(29,6)(23)(10,204)(194)(176)
Elements: 6,7,10,12,17,19,20,23,24,29,35,39,54,56,57,59,61, 113,115,162,170,176,184,194,196,204,208
Remarks: In cluster with 74. Transform CJB-l.
69
Order 27, reduced side 576
293 283
72 83
138139 144
42 ~ =t 28 4624
1 41 44I 26
145 154 149128
JDSII
Code: (293,283)(139,144) (138, 72, 83)(42,19,11)(8,12,28,46)(23, 4)(16)(44)(24,41) (26,154,5) (149) (145,17) (128)
Elements: 4,5,8,11,12,16,17,19,23,24,26,28,41,42,44,46,72, 83,128,138,139,144,145,149,154,283,293
Remarks: In cluster with 65. Transform V.
70
Order 27, reduced side 585
297 288
122 132156
175
25 24 ~rl2764
97 3771
62141
113 29 101'--- 69 70
51 40
Code: (297,288)(156,132)(175,122)(97,25)(24,17,27,64)(7,10) (71,141)(37)(113,62)(101)(1,70)(29,69)(51,11)(40)
CJB
Elements: 1,7,10,11,17,24,25,27,29,37,40,51,62,64,69,70,71, 97,101,113,122,132,141,156,175,288,297
Remarks: In cluster with 83, A139. Transforms I, II, Va.
71
Order 27, reduced side 587
275312
5984
34 1 25 132
i-----L
158 154 43 52 48
95
41 45 55 54 180
117
76 66 67 81
PJFITHW
Code: (312,275) (59, 84, 132) (158, 154) (34, 25) (9, 52,48) (43) (180) (95) (45, 55, 54)(117,41)(14,81)(76,10)(1,67)(66)
Elements: 1,9,10,14,25,34,41,43,45,48,52,54,55,59,66,67, 76,81,84,95,117,132,154,158,180,275,312
Remarks: In cluster with A162, A185. Transfonns I, Ib, IV.
72
Order 27, reduced side 588
159
218 211
59
100
48
132 145 47 ~:- 64 16327
5740 51
29 I
8960
225 214
149
AJWD
Code: (218, 159,211) (59, 100) (48, 163) (132, 145) (47, 37, 64) (10, 27) (57) (40, 51)(89,29,14)(1,16,225)(15)(214)(60)(149)
Elements: 1, 10, 14,15,16,27,29,37,40,47,48,51,57,59,60,64,89, 100,132, 145, 149,159,163,211,214,218,225
73
Order 27, reduced side 596
182 194220
57
I 11339 120
56
59206162
~454
11529 23
61
214196186
JDSII
Code: (220, ~82, 194) (57, 113, 12) (206) (162,39, 19) (20, 56) (59) (54, 115) (35, 24)(17,7)(61)(29,6)(23)(214)(10,196)(186)
Elements: 6,7,10,12,17,19,20,23,24,29,35,39,54,56,57,59,61, 113,115,162,182,186,194,196,206,214,220
Remarks: In cluster with 69. Transform CJB-1.
74
Order 27, reduced side 600
262
338
112150
57 66105 110 38
39 ~7448 tJ:
54 49
188157 152
103
AJWD
Code: (338,262)(112,150)(105,57,66, 110)(74,38)(48,9)(39,20, 16) (188)(5,11)(19,1)(6)(17)(157,54)(49,152)(103)
Elements: 1,5,6,9,11,16,17,19,20,38,39,48,49,54,57,66,74, 103,105,110,112,150,152,157,188,262,338
75
Order 27, reduced side 601
175 190
236
76 84
83 68 205153 92
70 8149 43
36 42
105
78212 206
96 87
JDSII
Code: (236,175,190)(76,84, 15)(205)(153,83)(68,8)(92)(70,81) (49,43)(212,11)(42,1)(206)(105,36)(78)(96,9)(87)
Elements: 1,8,9,11,15,36,42,43,49,68,70,76, 78,81,83,84,87,92,96,105,153,175,190,205,206,212,236
76
Order 27, reduced side 605
148181
276
33
115
51 64 214
69 83 r------r-124 38 125
5255 41 IT56 63
36 I
205 210190
JDSII
Code: (276,148, 181)(115,33)(214)(51,64)(124,69,83)(38, 13)(25,52)(55,14)(63)(41,56)(36,16)(20,210)(205,15)(190)
Elements: 13,14,15, 16,20,25,33,36,38,41,51,52,55,56,63,64,69,83,115, 124,148,181,190,205,210,214,276
Remarks: In cluster with CM, C65, C82. Transforms Ib, II, V, V, CJB-8, CJB-lO.
77
Order 27, reduced side 615
296319
78 129105 167136
~~ 4424 38
7188 91
53
160 52 49 152
103 99
51 50
JDSII
Code: (319,296)(129,167)(136,78,105)(34,44)(17, 88)(91, 38)(24,10)(71)(160)(53,152)(103,52,4)(49,99)(51,1)(50)
Elements: 1,4,10,17,24,34,38,44,49,50,51,52,53,71,78,88,91, 99,103,105,129,136,152,160,167,296,319
Remarks: In cluster with 93,97,98, A171, A175.
78
Order 27, reduced side 620
155197
268
42 .
113
101 114 239
166
88 5275
~ 5136
I--
~41186 184163
87
AJWD
Code: (268,155,197)(113,42)(239)(101,114,166)(88, 13)(75,52) (186,22,8,2)(6,51,184)(14)(36)(163)(5,46)(41)(87)
Elements: 2,5,6,8,13,14,22,36,41,42,46,51,52,75,87,88,101, 113,114,155,163,166,184,186,197,239,268
Remarks: In cluster with C70. Transform I.
79
Order 27, reduced side 620
281
339
126155
86125 128
29
39 I 47 97r---
33J:t-55 60
49 184156 22
11693
71
Code: (339,281) (126,155) (125, 86,128) (97, 29) (39, 47) (184) (156,8) (60,33,17,18)(55) (16, 1) (19) (49) (116) (93, 22) (71)
Elements: 1,8,16, 17,18,19,22,29,33,39,47,49,55,60,71,86,93, 97,116,125,126,128,155,156,184,281,339
Remarks: In cluster with A159. Transfonn I.
80
CJB
Order 27, reduced side 621
162 177
282
147
192
55 42
h2971
114 60I 8752 37
1 4336
~88
56
252225
144
AJWD
Code: (282,162,177)(147,15)(192) (55, 42, 71,114)(87,60) (13, 29) (52,16)(36,37,43)(252)(88)(31,6)(25,225)(56)(144)
Elements: 6, 13, 15, 16,25,29,31,36,37,42,43,52,55,56,60, 71, 87, 88, 114, 144, 147,162,177,192,225,252,282
81
Order 27, reduced side 627
283
344
128155
86123 135
6237 6649
77 7836 39 ~ 58
23
160 148112 111 96
Code: (344,283) (155,128) (123, 86,135) (66, 62) (37, 49) (77, 78) (160) (4,58) (39, 31)(148,36)(8,23)(112,1)(111,15)(96)
Elements: 1,4,8,15,23,31,36,37,39,49,58,62,66,77,78,86,96, 111,112,123,128,135,148,155,160,283,344
Remarks: In cluster with 94, A174. Transforms I, IlIa, V.
82
CJB
Order 27, reduced side 631
288
343
51 l:- 132156
69 70113 29
62 27 ~~2471 64
97 37
25
175 187147
122
JDSII
Code: (343,288) (132,156) (113, 51, 40, 69, 70) (11, 29) (62) (97, 1) (71) (64,27,17,24)(10,7)(187)(37)(175)(25,147)(122)
Elements: 1,7,10,11,17,24,25,27,29,37,40,51,62,64,69,70,71, 97,113,122,132,147,156,175,187,288,343
Remarks: In cluster with 71, A139. Transforms I, II, Va.
83
Order 27, reduced side 636
277
359
118159
56 6378
~41
162 J 7737 1 50
110
47 200164
11589
68
CJB
Code: (359,277)(118,159)(162,78,56,63)(77,41)(22, 14,20)(13, 50) (8,6) (2,37)(200)(110)(164)(115,47)(21,89)(68)
Elements: 2,6,8, 13, 14,20,21,22,37,41,47,50,56,63,68,77, 78, 89, 110, 115,118,159,162,164,200,277,359
Remarks: In cluster with A136. Transform I.
84
Order 27, reduced side 640
289
351
129160
109 97
14531
55 42 9836
73 f--26
37 30 22r--'-
33 41 191
144107 124
74
Code: (351,289)(129,160)(145, 109,97)(98,31)(55,42)(191)(36,73) (16,26)(144,37)(30,22,3)(19)(124)(41)(107,33)(74)
Elements: 3, 16, 19,22,26,30,31,33,36,37,41,42,55,73,74,97,98, 107, 109, 124,129,144,145,160,191,289,351
Remarks: In cluster with A176. Transform I.
85
cm
Order 27, reduced side 645
304341
77132
109 172
155
45 132
~3843
89
47 I 55
90 46
149169
102 105 120
JDSII
Code: (341,304) (132,172) (155,77,109) (45, 32)(89, 43) (13, 38, 90) (33,25) (3,169)(46)(8,55)(149,47)(15,120)(105)(102)
Elements: 3,8, 13, 15,25,32,33,38,43,45,46,47,55,77,89,90, 102, 105, 109, 120, 132,149,155,169,172,304,341
Remarks: In cluster with 92, A190, A214. Transforms I, Ib, II, III, IV, V.
86
Order 27, reduced side 646
302344
65105
~132
112 94138 27 [23130
35 9026 '-- 59
69 52
212
164 149121
Code: (344,302) (105, 65,132) (138,112,94) (28, 37) (12, 16) (7, 30) (90,27) (23) (212)(35,59)(26,69,17)(52)(164)(149)(121)
Elements: 7,12,16,17,23,26,27,28,30,35,37,52,59,65,69,90,94, 105,112,121,132,138,149,164,212,302,344
Remarks: In cluster with A151. Transform 1.
87
CJB
Order 27, reduced side 648
294
354
132162
89114
CJB
151
45'---
5329
69
50 ~
44 IW-~27
102
30
192
143
82111 120
Code: (354,294)(132, 162)(151, 114,89)(102,30)(50,39)(192)(45,69) (11,28)(44,17)(143,8)(27,18)(53)(120)(29,111)(82)
Elements: 8, 11, 17, 18,27, 28, ~9, 30, 39,44,45,50,53,69,82,89, 102,111,114,120,132,143,151,162,192,294,354
Remarks: In cluster with A196. Transform 1.
88
Order 27, reduced side 650
161
253 236I
72 89
30 34 37 I
56 r~I
I105172 90
18499
I
95 10029
242213 195
JDSII
Code: (253,236,161)(72,89)(37,18,17)(30,172,34)(1, 105)(19) (184,56,13)(43)(90)(99)(5,100)(95)(29,242)(213)(195)
Elements: 1,5, 13, 17, 18, 19,29,30,34,37,43,56,72,89,90,95,99, 100,105,161,172,184,195,213,236,242,253
Remarks: In cluster with C79, C87. Transform Ib, II, V.
89
Order 27, reduced side 656
181227
248
46
135
89
114134 184
95129
94 42 3874
H25 3432
245
200 211
AJWD
Code: (248,181,227)(135,46)(89,184)(114, 134)(129,95)(94,20)(74,42,38)(34,245)(13,25)(32,10)(1,12)(11)(211)(200)
Elements: 1,10,11,12,13,20,25,32,34,38,42,46,74,89,94,95, 114,129,134,135,181,184,200,211,227,245,248
Remarks: In cluster with 111, C75, C80. Transforms I, lb, II, III, IV, V.
90
Order 27, reduced side 656
292
364
111
18171
133 41160 ~ 70
62 50
3968
47
~~37 30 183159
132 115
67
AJWD
Code: (364,292) (111,181) (160,133,71) (41, 70) (62, 9) (50) (68,183) (3,47) (39,159)(132,28)(16,23)(115)(37,7)(30)(67)
Elements: 3,7,9,16,23,28,30,37,39,41,47,50,62,67,68,70,71, 111,115,132,133,159,160,181,183,292,364
91
Order 27, reduced side 660
304
356
132172
102 105149
43
47 I 55 89
90 46
~3845 132 184
155135
10977
Code: (356,304) (172, 132) (149,102,105) (43, 89) (47, 55) (90,15) (184, 3) (46) (155,33,8)(25,38)(135)(45,13)(32,109)(77)
Elements: 3,8, 13, 15,25,32,33,38,43,45,46,47,55,77,89,90, 102, 105,109, 132, 135,149,155,172,184,304,356
Remarks: In cluster with 86, A190, A214. Transforms I, Ib, II, III, IV, V.
92
CJB
Order 27, reduced side 660
296
364
129
51 50167
103
160 52 49 38
9153
71 88
24
~144 197
136 144105
78
cm
Code: (364,296)(167,129)(160, 103,51,50)(1,49)(52)(38,91)(4, 197,53)(71,88)(144)(136,24)(10,44,17)(34)(105)(78)
Elements: 1,4, 10, 17,24,34,38,44,49,50,51,52,53, 71, 78,88,91, 103, 105, 129, 136,144,160,167,197,296,364
Remarks: In cluster with 78,97,98, A171, A175.
93
Order 27, reduced side 663
319344
112 111 96
86
135 12323
37 36 39 ~ 5849
77 78
66 62
184 196155
128
JDSII
Code: (344,319)(112,111,96)(135,86, 123)(15,23,58)(49,37)(1,78,39,8)(36,77)(31)(196)(66,4) (62)(184)(155)(128)
Elements: 1,4,8,15,23,31,36,37,39,49,58,62,66,77,78,86,96, 111,112,123,128,135,155,184,196,319,344
Remarks: In cluster with 82, A174. Transforms I, IlIa, V.
94
Order 27, reduced side 664
303
361
137166
96133 132
2937
59 10832 47R:- 53
"--------r;;- 39 195170
98 11685
Code: (361,303) (137,166) (133, 96,132) (108,29) (37, 59) (195) (32, 53, 47) (170) (50,9) (41) (39,8) (20, 33) (116) (98, 13) (85)
Elements: 8,9,13,20,29,32,33,37,39,41,47,50,53,59,85,96,98, 108,116,132,133,137,166,170,195,303,361
Remarks: In cluster with A223. Transfonn I.
95
CJB
Order 27, reduced side 666
293
373·
114
179
83117 49 65
17334
82 6656
95 R;;-53 194
128120
67 81 76
JDSII
Code: (373,293) (114, 179) (173, 117,83) (49, 65) (34,82, 16) (66, 194) (95,56) (20,128)(120,53)(44,12)(32)(14,81)(76)(67)
Elements: 12,14, 16,20,32,34,44,49,53,56,65,66,67,76,81,82, 83,95,114,117,120,128,173,179,194,293,373
96
Order 27, reduced side 668
296
372
129167
5378
105136 38
~~ 4424 144
71 88
205
160 52 49
103 99
51 50
JDSII
Code: (372,296)(129,167)(136, 78,105,53)(144,38)(34,44)(205)(17,88)(24,10)(71)(160)(103,52,4)(49,99)(51,1)(50)
Elements: 1,4,10,17,24,34,38,44,49,50,51,52,53,71,78,88,99, 103,105,129,136,144,160,167,205,296,372
Remarks: In cluster with 78,93,98, AI71, A175.
97
Order 27, reduced side 671
319352
7850 51 105
13699
~4~ 44152 49 5224
71 8853
91
38
216
167 159129
JDSH
Code: (352,319) (136, 78,105) (152, 99, 50, 51) (34, 44) (49, 1) (52) (17, 88) (24,10)(71)(53,91,4)(216)(167,38)(159)(129)
Elements: 1,4,10,17,24,34,38,44,49,50,51,52,53,71,78,88,91, 99,105,129,136,152,159,167,216,319,352
Remarks: In cluster with 78,93,97, A171, A175.
98
Order 27, reduced side 672
345 327
86116 147
143 180
129
57 I2846
71 544425 9336 f--
1--'- 3951
184165
27140
10578
AJWD
Code: (345,327)(180,147)(143,86, 116)(57,29)(28, 1)(71,46)(54,93)(184,44)(25,165,36)(15,39)(140)(51)(27,105)(78)
Elements: 1,15,25,27,28,29,36,39,44,46,51,54,57,71, 78,86,93, 105,116,140,143,147,165,180,184,327,345
99
Order 27, reduced side 674
321353
87 133105
188161
69 4756 67 86 I-------T
39 1 3157 37 1 5346
160 165134
103 112
JDSII
Code: (353,321)(133, 188)(161, 105,87)(18,69)(86,47)(56,67)(39,8)(16,53)(31,165)(160,57)(46,37)(22,134)(112)(103)
Elements: 8,16,18,22,31,37,39,46,47,53,56,57,67,69,86,87, 103,105,112,133,134,160,161,165,188,321,353
Remarks: In cluster with 114, A212, A233. Transforms I, Ib, II, III, IV, V.
100
Order 27, reduced side 676
169
263 244
94 75
83
103 108
165 44 l39 217
6241 36 29 I34
9256 63
248213 215
AJWD
Code: (263,169,244) (94, 75) (19, 83,217) (165,103, 108) (44,39) (62, 41) (5,34) (36,92,29)(63)(21,56)(248)(2,215)(213)
Elements: 2,5,19,21,29,34,36,39,41,44,56,62,63,75,83,92,94, ]03,108,165,169,213,215,217,244,248,263
101
Order 27, reduced side 676
160
231
285
79 81
114 109 85 83
116 261 42169
11094119 68
53 6330
222242
212
JDSII
Code: (285,231,160)(79,81)(114, 109,8)(85,2)(83)(169, 116)(16,42,110)(5,94,26)(119)(68)(53,63)(30,242)(222)(212)
Elements: 2,5,8, 16,26,30,42,53,63,68,79,81,83,85,94, 109, 110, 114,116, 119, 160,169,212,222,231,242,285
Remarks: In cluster with 117, C78, C81, C95.
102
Order 27, reduced side 676
292
384
123169
69 72108 46
135 77
66 47 ~
~37 r30 53
215184
157120
JDSII
Code: (384,292) (123, 169) (135, 69, 72, 108) (77, 46) (66,3) (47, 28) (215) (19, 9) (1,184)(10)(23,53)(157,37,7)(30)(120)
Elements: 1,3,7,9,10,19,23,28,30,37,46,47,53,66,69,72,77, 108,120,123,135,157,169,184,215,292,384
103
Order 27, reduced side 677
206 194
277
tR 402871
95 137
24 97
143181 119
89
145
38 56
257219 201
AJWD
Code: (277,206,194)(17,40,137)(71,95,28,12)(7,10)(16,3) (13) (97)(181,143,24)(119)(89,145)(38,257,56)(219)(201)
Elements: 3,7, 10, 12, 13, 16, 17,24,28,38,40,56,71,89,95,97, 119, 137,143, 145, 181,194,201,206,219,257,277
104
Order 27, reduced side 677
344 333
67 4956
h-;-80
118 137
170
128124
52 66 51
1-....-86
59 3545
163 149 140104 121
AJWD
Code: (344,333)(67,49,80,137)(170,118,56)(18,31)(128,13)(124) (52,66)(51,86)(163,59)(16,35)(45,149)(140)(121)(104)
Elements: 13, 16, 18,31,35,45,49,51,52,56,59,66,67,80,86, 104, 118, 121, 124,128,137,140,149,163,170,333,344
105
Order 27, reduced side 678
312
366
5477
23
181
121 123153 100
5630
6524
-55 29 61
189 185159
71 74
AJWD
Code: (366,312)(54,77,181)(121,153, 123,23)(100)(65,56)(30, 189,4)(185)(24,159) (19, 61) (55,10) (29) (16, 13) (74) (71)
Elements: 4,10,13,16,19,23,24,29,30,54,55,56,61,65,71,74, 77, 100,121,123,153,159,181,185,189,312,366
106
Order 27, reduced side 679
342 337
6897 105
94
145 261 42 170
30 -L-48 49 '-- 74
44 5891
50
192 174 172141
AJWD
Code: (342,337)(5,94,68,170)(145,97,105)(26,42)(30,74, 16)(48, 49)(91,14)(58)(44)(192,1)(50)(174,2)(172)(141)
Elements: 1,2,5,14,16,26,30,42,44,48,49,50,58,68,74,91,94, 97, ]05, 141,145,170,172,174,192,337,342
]07
Order 27, reduced side 679
296
383
51 59I--
~36
231 186
81 94124 119 75
43 I 38 2569 64
177197
172133
CJB
Code: (383,296)(51,59,186)(36,15)(7,52)(22)(124,81, 119,94, 1) (23)(75)(43,38)(25,69)(64,197)(5,177)(172)(133)
Elements: 1,5,7,15,22,23,25,36,38,43,51,52,59,64,69,75,81, 94,119,124,133,172,177,186,197,296,383
Remarks: In cluster with SPSR 25:296x592. Transform VIII.
108
Order 27, reduced side 680
177
239264
85 92
114 125 cl~ 738947
57175
86106 12095 98
241221 218
AJWD
Code: (264,239,177)(85,92)(114,125)(45,33,7) (175, 89)(26, 73) (12,47)(57)(120)(86,106,11)(95,98)(241,20)(221)(218)
Elements: 7,11,12,20,26,33,45,47,57,73,85,86,89,92,95,98, 106,114,120,125,175,177,218,221,239,241,264
109
Order 27, reduced side 680
312
368
61 64
52 47 25 53 187
157 159
107 70
7667 48
181155 153
86 105
AJWD
Code: (368,312)(61,64,187)(157,159,52)(47, 14)(11,53)(25)(8,17) (107)(70)(76,181) (155, 2) (153, 67, 48) (19, 105) (86)
Elements: 2,8,11,14,17,19,25,47,48,52,53,61,64,67,70,76,86, 105,107,153,155,157,159,181,187,312,368
110
Order 27, reduced side 690
181227
282
46
13589
34184
114134
95
163
94 42 3874
32 H25
279
200 211
AJWD
Code: (282,181,227) (135,46) (89,184) (114,134,34) (163, 95) (94, 20) (279) (74,42,38)(13,25) (32, 10)(1, 12)(11) (211)(200)
Elements: 1,10,11,12,13,20,25,32,34,38,42,46,74,89,94,95, 114,134,135,163,181,184,200,211,227,279,282
Remarks: In cluster with 90, C75, C80. Transforms I, Ib, II, III, IV, V.
111
Order 27, reduced side 692
300
392
127173
69 71
136116 46
~4081
67261 I
39 45 41
219
164184
125
AJWD
Code: (392,300)(127,173)(136,69,71, 116)(81,46)(67,2)(33,40) (219)(26,7)(19,23,5)(18,184)(45)(41)(164,39)(125)
Elements: 2,5,7,18,19,23,26,33,39,40,41,45,46,67,69,71,81, 116,125,127,136,164,173,184,219,300,392
112
Order 27, reduced side 693 AJWD
349 344
165189
154165
5266
40 3111-24--'-r- --.---'---i f----l.-....-------i
50 83
91 ~44 38
155 164
88 85 89112
Code: (349,344) (5, 154, 185) (165, 189){40, 83, 31) (91, 50, 24) (52, 164) (32,155,66)(44,6)(38)(23,112)(89)(88,3)(85)
Elements: 3,5,6,23,24,31,32,38,40,44,50,52,66,83,85,88,89, 91,112,154,155,164,165,185,189,344,349
113
Order 27, reduced side 696
321
375
133
103188
112160
47
57 46 371 53
h-- 86
31 I 39
56 6769
187161 156
105 87
Code: (375,321)(188, 133)(160, 103,112)(47,86)(57,46)(37,53,22) (8,39)(187,31)(67,16)(161,56)(69)(156)(105,18)(87)
Elements: 8, 16, 18,22,31,37,39,46,47,53,56,57,67,69,86,87, 103,105, 112,133,156,160,161,187,188,321,375
Remarks: In cluster with 100, A212, A233. Transforms I, Ib, II, III, IV, V.
114
CJB
Order 27, reduced side 703
307
396
119
188
5828L
........... 69174 164 32
76
30 8146
41 51208
133 143 12792
AJWD
Code: (396,307)(119,188)(174,164,58)(28,22,69)(7, 15)(76,9, 1) (8)(32)(81,208)(30,46)(51,143)(133,41)(127)(92)
Elements: 1,7,8,9,15,22,28,30,32,41,46,51,58,69,76,81,92, 119,127,133,143,164,174,188,208,307,396
115
Order 27, reduced side 704
323
381
69 75
74 63179
90 88129 81
5545 41 825892 27
49
194 202167
141
JDSII
Code: (381,323) (69, 75,179) (90,88,129,74) (63, 6) (81) (55, 82) (2, 45,41) (92) (58,23) (202) (4,194,27) (49) (167) (141)
Elements: 2,4,6,23,27,41,45,49,55,58,63,69,74, 75,81,82,88,90,92,129,141,167,179,194,202,323,381
116
Order 27, reduced side 706
160
231
315
79 81
114 109 85 83
30261 42
116 11094169 68
149
53 63
272
222 212
JDSII
Code: (315,231,160) (79,81) (114, 109, 8) (85, 2) (83) (169, 116,30) (16,42, 110) (5,94,26)(149)(68)(53,63)(272)(222)(212)
Elements: 2,5,8, 16,26,30,42,53,63,68,79,81,83,85,94, 109, 110, 114, 116, 149, 160,169,212,222,231,272,315
Remarks: In cluster with 102, cn, C81, C95.
117
Order 27, reduced side 708
179
235
294
56
123
67115 109
48111
4465175 150 61 -r-
102
64 4784 86
43
239 256213
AJWD
Code: (294,179,235)(123,56)(67,115, 109)(175, 111,8)(150,48)(44,65)(102,61)(23,21)(64,47)(86)(84)(256,4~)(239)(213)
Elements: 8,21,23,43,44,47,48,56,61,64,65,67,84,86, 102, 109, 111, 115, 123, 150,175,179,213,235,239,256,294
118
Order 27, reduced side 708
177
228
303
51
126
99
24 18076 66
94 4281
16937 49 I 59
39
--75
56
10864
300
236
172
AJWD
Code: (303,177,228) (126, 51) (99,180) (169,94,76,66,24) (42, 81) (l0, 59, 39) (37,49)(75,19)(300)(56)(108)(236,64)(172)
Elements: 10,19,24,37,39,42,49,51,56,59,64,66,75,76,81,94, 99,108,126,169,172,177,180,228,236,300,303
119
Order 27, reduced side 708
342366
4431 I
~ 53132
138166
177
95 34
51 98
'--- 87 385763
27 200165
117 13690
AJWD
Code: (366,342) (44,132, 166) (177,138,31,20) (11, 53) (42) (95) (98, 34) (51,87) (200)(57,38) (165,12) (63) (136) (27,117) (90)
Elements: 11, 12,20,27,31,34,38,42,44,51,53,57,63,87,90,95, 98,117,132,136,138,165,166,177,200,342,366
120
Order 27, reduced side 709
299
410
61 73f--
49 165
8548
142 12251 I147 4475
128
95
157 177152
106 117
AJWD
Code: (410,299)(61,73,165)(49,12)(85)(1,48)(147, 142, 122)(75,51,7)(44,128)(95)(20,177)(5,157)(152)(11,117)(106)
Elements: 1,5,7,11,12,20,44,48,49,51,61,73,75,85,95,106, 117,122,128,142,147,152,157,165,177,299,410
121
Order 27, reduced side 716
199240
277
77122 36
98 11354 204
17968
81 57 1 4359 ~8 55
100 84
260 272
184
JDSH
Code: (277,199,240) (122, 77) (36, 204) (113) (179, 98) (54, 68) (81, 57, 14) (43, 59, 38,55)(21,17)(100)(4,272)(84) (260)(184)
Elements: 4,14,17,21,36,38,43,54,55,57,59,68,77,81,84,98, 100,113,122,179,184,199,204,240,260,272,277
122
Order 27, reduced side 716
343373
138113 108
152 205
3974 79 76 91
37
58 1 43 44 ~~191
168156
101 100
AJWD
Code: (373,343) (138, 205) (152, 113, 108) (79, 76, 91) (39, 74) (191) (37, 168) (3, 58,15) (156) (43, 44,19) (6, 31) (25) (101) (100)
Elements: 3,6,15,19,25,31,37,39,43,44,58,74,76,79,91,100, 101,108,113,138,152,156,168,191,205,343,373
123
Order 27, reduced side 724
365 359
43 49 I 63 7682 99147 78 165
64
65 89
9472
9254
212 200166 146
AJWD
Code: (365,359) (6, 49, 63, 76,165) (147, 82, 99, 43) (78, 14) (64,13) (89) (65,17) (94,22)(72,92)(212)(54,200)(166)(146)
Elements: 6,13,14,17,22,43,49,54,63,64,65,72,76, 78,82,89,92,94,99,146,147,165,166,200,212,359,365
124
Order 27, reduced side 728
213265 250
I
108 105
56130 120
209 80 87 102
40
100 11073
94 8260
28
254 248226
AJWD
Code: (265,213,250) (108,105) (130,120) (209, 56) (3, 102) (80,87) (10, 110) (40,100)(73,7)(94)(82,60)(254,28)(22,248)(226)
Elements: 3, 7, 10,22,28,40,56,60, 73, 80, 82, 87, 94, 100, 102, 105, 108, 110, 120, 130,209,213,226,248,250,254,265
125
Order 27, reduced side 731
224 227
280
67 54 51103
89 17678
42 I105
61180
I
91 99 8580 65
131
66
271 263
197
JDSII
Code: (280,224,227) (67,103,54) (51,176) (105) (l80, 89,11) (78) (42, 61) (91, 99,19)(85,20)(80)(65,131)(271)(263,66)(197)
Elements: 11,19,20,42,51,54,61,65,66,67,78,80,85,89,91,99, 103,105,131,176,180,197,224,227,263,271,280
126
Order 27, reduced side 732
206 212
314
200218
129
18546
56 I 64 r:- 130106
136
3988 - 30
49
233196
166137
AJWD
Code: (314,206,212) (200,6) (218) (185, 129) (46, 130,24) (106, 136) (56,64,9) (55)(233,8)(88,39)(10,196,30)(49)(166)(137)
Elements: 6,8,9,10,24,30,39,46,49,55,56,64,88,106,129,130, ]36, ]37, 166, 185,196,200,206,212,218,233,314
127
Order 27, reduced side 732
206 212
314
200218
113 t
201
2546
88 13010671 136
64 I 56 ~3 30
217196
153 166
JDSII
Code: (314,206,212) (200, 6) (218) (201,113) (46,130,24) (88, 25) (106, 136) (71) (217,64,8)(56,23)(10,196,30)(33)(166)(153)
Elements: 6,8, 10,23,24,25,30,33,46,56,64, 71, 88, 106, 113, 130, 136, 153, 166, 196,200,201,206,212,217,218,314
128
Order 27, reduced side 733
324
409
81 63
~
3~ 5327 45 180
9041
72157 147 46
57 74 69
229
167 177 160
AJWD
Code: (409,324)(81,63,180)(18,45)(19,53,27)(157, 147,90, 15)(34) (72)(41,46)(57,74)(69,229)(10,177,17)(167)(160)
Elements: 10,15,17,18,19,27,34,41,45,46,53,57,63,69,72, 74,81,90,147,157,160,167,177,180,229,324,409
129
Order 27, reduced side 736
191212
333
5332
138
85180
63
152 156185
117 126
33
49 4092 86
43 46
251218
135 132
AJWD
Code: (333,191,212)(138,53)(32,180)(85)(4, 156,63)(185, 152)(117,126)(33,251,24)(92,49)(218)(40,86)(43,46)(135)(132)
Elements: 4,24,32,33,40,43,46,49,53,63,85,86,92,117,126, 132, 135,138, 152, 156,180,185,191,212,218,251,333
130
Order 27, reduced side 744
222272
250
102 12052 89
161
1-'--66220 43136 118
55 I 48 I 42
32 12583
284252
208
AJWD
Code: (272,222,250)(102,120)(89,161)(220,52)(136,18)(23,66) (118,20)(43)(55,48,6)(42,125)(7,83)(32,284)(252)(208)
Elements: 6,7,18,20,23,32,42,43,48,52,55,66,83,89,102,118, 120,125,136,161,208,220,222,250,252,272,284
131
Order 27, reduced side 744
222272
250
102 12052 101
149
220 136rs11 42 I 48
11867 66
32 137
71
284252
208
AJWD
Code: (272,222,250)(102,120)(101,149)(220,52)(136,18)(118,20) (11,42,48) (31)(67,6)(66,137)(32,284,5)(71)(252)(208)
Elements: 5,6, 11, 18,20,31,32,42,48,52,66,67, 71, 101, 102, 118, 120, 136, 137, 149,208,220,222,250,252,272,284
132
Order 27, reduced side 752
210251
291
41 I 47~
12253
102 94 90
62 ~
22998 126 135
164
74
285
232 235
JDSII
Code: (291,251,210) (41, 47, 122) (102, 94, 90, 6) (53) (229, 62) (31,22) (9, 135) (4,126)(98)(164)(74,24)(285)(3,235)(232)
Elements: 3,4,6,9,22,24,31,41,47,53,62,74,90,94,98,102,122, 126,135,164,210,229,232,235,251,285,291
133
Order 27, reduced side 752
208245
299
52 56100
4879
46111 102 - 226
57 68188
77 65 60
136
70
265 281
206
AJWD
Code: (299,208,245)(100,52,56) (19, 226)(48,4) (79)(188,111) (102,46)(11,68)(57)(77,136)(65,60)(5,281)(70)(265)(206)
Elements:. 4,5,11, 19,46,48,52,56,57,60,65,68,70,77,79,100, 102,111, 136, 188,206,208,226,245,265,281,299
134
Order 27, reduced side 755
216
276 263
60 47
109
57 71 93I-- 31
43 29 1 78 217208 271 5645
1--...... 124
63143
66
271 275
209
AJWD
Code: (276,216,263)(60,109,47)(93,217)(208,57,71)(78,31) (43, 14)(29,56) (124)(45,27)(18,143)(63)(66,275)(271)(209)
Elements: 14,18,27,29,31,43,45,47,56,57,60,63,66,71,78,93, 109,124,143,208,209,216,217,263,271,275,276
135
Order 27, reduced side 755
215
278 262
88127 41
64
129 221214 101 90
49 36 rd42 51103
56 61
263 272220
JDSII
Code: (278,215,262) (127, 88) (41, 221) (214, 64) (129) (101, 90) (23, 42, 103,51) (49,36,16)(4,19)(20)(61)(56)(272)(263)(220)
Elements: 4,16,19,20,23,36,41,42,49,51,56,61,64,88,90,101, 103,127,129,214,215,220,221,262,263,272,278
136
Order 27, reduced side 755
189
262304
78111
37 41 38
56 5398
141 224183 55 54
8545
12296
268 269218
AJWD
Code: (304, 189,262) (78, 111) (38, 224) (37, 41) (8, 141) (183, 98, 56,4) (53) (55, 1)(54)(85,13)(122)(96,45)(269)(268)(218)
Elements: 1,4,8,13,37,38,41,45,53,54,55,56,78,85,96,98,111, 122,141,183,189,218,224,262,268,269,304
137
Order 27, reduced side 764
199240
325
4167
91r-----'"- 50
43r-- 4627
119 23173
148193
62
45 l~130
6629
293246
225
JDSII
Code: (325, 199,240) (67,91,41) (50, 231) (43, 24) (46, 119) (16, 27) (193, 148) (73)(130,62)(293)(45,37,66)(8,29)(246)(225)
Elements: 8,16,24,27,29,37,41,43,45,46,50,62,66,67,73,91, 119,130,148,193,199,225,231,240,246,293,325
138
Order 27, reduced side 807
216259
332
3871
107 33 28
13298 236
137
20448 5452 76
67114 110
312271
224
AJWD
Code: (332,216,259)(107, 71,38)(33,5)(28,236)(132)(9,98)(204,137)(2,54,76)(48,52)(67,114,4)(110)(312)(271)(224)
Elements: 2,4,5,9,28,33,38,48,52,54,67,71, 76, 98, 107, 110, 114, 132, 137, 204,216,224,236,259,271,312,332
139
Order 27, reduced side 832
388444
190 198114 131
199
97 80 68 65
12587
111
6083
6333
189177129 135
106 96
Code: (444,388)(190,198)(114,131, 199)(97,17)(80,68)(65, 125)(87,111)(189,83,60) (177) (63, 24) (135) (23,129,33)(106)(96)
CJB
Elements: 17,23,24,33,60,63,65,68,80,83,87,96,97,106,111, 114,125,129,131,135,177,189,190,198,199,388,444
Remarks: In cluster with 158, A256. Transforms I, lIe, Va.
140
Order 27, reduced side 835
228287
320
59
169
4776
I29h 161185
197
121171
96 113137
318267 250
JDSII
Code: (320,228,287)(169,59)(185,161)(197,76,47)(29, 18)(11,7) (4,3)(1,2)(121)(171)(24,137)(96,113)(318)(267)(250)
Elements: 1,2,3,4,7,11,18,24,29,47,59,76,96,113,121,137, 161,169,171,185,197,228,250,267,287,318,320
141
Order 27, reduced side 844
392
452
181211
207245
30
151
3868
101 I 51 58 241I 3150
'-- 147120
84 96 8967
Code: (452,392)(181,211)(207,245)(151,30)(241)(101,68,38)(27, 51,147,58)(3,24)(31,120)(50,21)(96)(89)(84,17)(67)
Elements: 3,17,21,24,27,30,31,38,50,51,58,67,68,84,89,96, 101,120,147,151,181,207,211,241,245,392,452
Remarks: In cluster with A341, A373. Transforms I, Ib, IV.
142
CJB
Order 27, reduced side 855
432 423
108
171 153 184
63 1 45239
75105 83
~101
46
N4~252193
165 14798
Code: (432,423) (184, 239) (171,108,153)(63,45)(18,75,105)(252) (83,101)(43,32)(46,193)(23,165)(11,21)(54)(147)(44)(98)
Elements: 11, 18,21,23,32,43,44,45,46,54,63,75,83,98, 101, 106, 108,147, 153, 165,171,184,193,239,252,423,432
Remarks: In cluster with A288. Transform 1.
143
CJB
Order 27, reduced side 855
404451
101119
184129 151171 83
42 ~19 48137
r---- 5867
93
267233
195160
CJB
Code: (451,404)(119,101,184)(171, 129, 151)(18,83)(137)(42,22, 17,48)(267)(5,12)(20,7)(93,58)(19)(233)(67)(195)(160)
Elements: 5,7,12,17,18,19,20,22,42,48,58,67,83,93,101,119, 129,137,151,160.171,184,195,233,267,404,451
Remarks: In cluster with A262. Transform I.
144
Order 27, reduced side 860
383
477
168215
128160
189 47
12161 67
75 8556
~ 262
37141 194 188138
78
Code: (477,383) (168, 215) (160, 189, 128) (121, 47) (262) (61, 67) (75, 85) (56, 194)(188) (33, 29,13) (3, 138) (16) (4, 41) (37) (78)
Elements: 3,4,13,16,29,33,37,41,47,56,61,67,75,78,85,121, 128,138,160,168,188,189,194,215,262,383,477
Remarks: In cluster with A270. Transform 1.
145
CJB
Order 27, reduced side 872
363
509
165198
1122 W- 108
200 187 75 53127
65 57
50 I 63236
163 176 184
113
Code: (509,363) (198, 165) (200, 187, 122) (29, 28, 108) (1, 27) (4,26) (127,75) (53)(65,57)(236)(184)(13,63,176)(163,50)(113)
Elements: 1,4, 13,26,27,28,29,50,53,57,63,65, 75, 108, 113, 122, 127, 163, 165, 176,184,187,198,200,236,363,509
Remarks: In cluster with A284. Transform I.
146
CJB
Order 27, reduced side 876
404
472
213 191
145 144183
38 63 81 80107 f-- 169
45 155
221
152179 51 57
104 11253 55
PJFITHW
Code: (472,404)(213,191)(183,145,144)(22, 169)(63,81)(38, 107) (80,155)(221)(45,18)(179)(152)(57,112)(104,51)(2,55)(53)
Elements: 2,18,22,38,45,51,53,55,57,63,80,81,104,107,112, 144,145,152,155,169,179,183,191,213,221,404,472
Remarks: In cluster with A300. Transform 1.
147
Order 27, reduced side 885
405
480
102132
171
120133
69 I175 36
185129
55 6589 97 90
111 105
230 220 219
109 107
CJB
Code: (480,405)(171,102,132)(175,120,185)(69, 33)(3,129)(36)(89,97,90)(55,65)(230)(220,111,8)(219)(105)(109,2)(107)
Elements: 2,3,8,33,36,55,65,69,89,90,97, 102, 105, 107, 109, 111, 120, 129, 132, 171,175,185,219,220,230,405,480
Remarks: In cluster with 160, A266. Transforms II, V, CJB-28.
148
Order 27, reduced side 892
400
492
177223
143 16318646
43131
100 5357 49 64 87
82 g269
157184
132 150
cm
Code: (492,400) (177,223) (143,186,163)(131,46)(269)(100,43)(23, 87,53)(57,82,49,64)(184)(33,16)(157)(1,150)(17)(132)
Elements: 1,16,17,23,33,43,46,49,53,57,64,82,87,100,131, 132,143,150,157,163,177,184,186,223,269,400,492
Remarks: In cluster with A319. Transform 1.
149
Order 27, reduced side 895
388
507
100 123165
77
139 ~ 146189 179 93
57 92
40
249 238199 209
CJB
Code: (507,388) (165, 100, 123) (77, 23) (189, 179,139) (146) (93, 36, 15, 9, 12) (6, 3)(92)(21)(57)(40,249)(238)(10,209)(199)
Elements: 3,6,9,10,12,15,21,23,36,40,57,77,92,93,100,123, 139,146,165,179,189,199,209,238,249,388,507
Remarks: In cluster with A259. Transform II.
150
Order 27, reduced side 897
396
501
6899
t--.---37 31
22973
113 130165 '----r---
187 33 40........f-l- 5236
98 87
272
209 231185
CJB
Code: (501,396) (68, 99,229) (37,31) (130) (187, 165,73, 113) (33, 40) (23, 10) (3,52,98)(13)(87,272)(36)(22,231)(209)(185)
Elements: 3,10,13,22,23,31,33,36,37,40,52,68,73,87,98,99, 113,130,165,185,187,209,229,231,272,396,501
Remarks: In cluster with SPSR 25:396x792. Transform VIII.
151
Order 27, reduced side 900
407
493
78122
70 207
128 37
178 ~~ 85195
50 ~H 46113
60
286
212 229173
TRW
Code: (493,407)(78,122,207)(8,70)(195,178, 128)(37,85)(59, 11) (48)(113,286)(50,32,46)(18,14)(60)(17,229)(212)(173)
Elements: 8,11,14,17,18,32,37,46,48,50,59,60,70,78,85,113, 122,128,173,178,195,207,212,229,286,407,493
Remarks: In cluster with SPSR 25:407x814. Transform VIII.
152
Order 27, reduced side 900
404
496
199 205
124176 196
50 4452 72
149 1619460
~~ 54228 20861 31
148 13087 99
Code: (496,404) (199,205) (176,124,196) (149, 50) (44,161) (52, 72) (94) (228) (208,60)(40,54)(148,61)(31,130)(26,14)(99)(87)
Elements: 14,26,31,40,44,50,52,54,60,61,72,87,94,99,124,130, 148,149,161,176,196,199,205,208,228,404,496
Remarks: In cluster with 177, A370. Transforms I, IIIa, V.
153
CJB
Order 27, reduced side 900
401
499
176225
90120 136153
63 L 49
H: 12799 83 69
248274
182 196
Code: (499,401) (176, 225) (153, 90,120,136) (127, 49) (63, 27) (19,8) (5,99,16) (13)(274)(17,2)(83,69)(15)(248)(196)(182)
Elements: 2,5,8,13,15,16,17,19,27,49,63,69,83,90,99,120,127, 136,153,176,182,196,225,248,274,401,499
Remarks: In cluster with A312. Transform 1.
154
CJB
Order 27, reduced side 905
431474
130 137164
231 243123 116 f--~
59 133
33 4431
~ol 69
200 221188 177
119
Code: (474,431)(130,137,164)(231,243)(123, 7)(116,28)(1,30,133) (29)(59)(33,221,44)(200,31)(19,69,188)(177)(50)(119)
cm
Elements: 1,7,19,28,29,30,31,33,44,50,59,69,116,119,123, 130,133,137,164,177,188,200,221,231,243,431,474
Remarks: In cluster with 167, 194, A277, A346.
155
Order 27, reduced side 906
414
492
145 136 133
129 31 34181 182 f---
96 9965
52 15477
39
119101
233260
193
107 113
PJPITHW
Code: (492,414) (145, 136, 133) (181, 129, 182) (34, 99) (9, 96, 31) (154) (65) (52, 77)(260)(233)(24,119,39)(101)(193)(6,113)(107)
Elements: 6,9,24,31,34,39,52,65,77,96,99,101,107,113,119,129, 133,136,145,154,181,182,193,233,260,414,492
Remarks: In cluster with A324. Transform 1.
156
Order 27, reduced side 908
403
505
176227
120161
224 51
41 12579
108 94
4533 278~ 61
204179
~~134 r-- 37
63 50
Code: (505,403) (176, 227)(224,161,120)(125,51)(41,79)(278) (108, 94)(204)(179,45)(33,61)(134,19)(52)(24,37)(63,13)(50)
Elements: 13, 19,24,33,37,41,45,50,51,52,61,63, 79, 94, 108, 120, 125, 134, 161, 176,179,204,224,227,278,403,505
Remarks: In cluster with A311. Transform I.
157
CJB
Order 27, reduced side 910
466 444
96114 131106
135 129199
3363
83 97 80 6860
111 87 12565
255 267
198 190
Code: (466,444) (114,131,199) (135, 96,129,106) (97,17) (63, 33) (23, 83) (80, 68)(125,60) (111, 24) (87) (267) (65, 255) (198)(190)
Elements: 17,23,24,33,60,63,65,68,80,83,87,96,97,106,111, 114,125,129,131,135,190,198,199,255,267,444,466
Remarks: In cluster with 140, A256. Transforms I, lIe, Va.
158
CJB
Order 27, reduced side 913
260296
357
36
224
127
230 332
160191
57
47173
116 101
28576 75 86 238
153
77 78 82
AJWD
Code: (357,260,296)(224,36)(332)(230,127)(160,191)(173, 57)(47, 285)(116,101)(238)(15,86)(153,76,75)(4,82)(1,78)(77)
Elements: 1,4,15,36,47,57,75,76,77,78,82,86,101,116,127, 153, 160,173,191,224,230,238,260,285,296,332,357
159
Order 27, reduced side 915
435480
109 107
120 219185 175
111 105
65 55
89 97 90129
136250 260 69 I33
171132
102
JDSII
Code: (480,435)(109;107,219)(185,120, 175)(2, 105)(111)(65,55)(8,97)(90,129)(260,89)(250)(171,69,36)(33,3)(132)(102)
Elements: 2,3,8,33,36,55,65,69,89,90,97,102,105,107,109,111, 120,129,132,171,175,185,219,250,260,435,480
Remarks: In cluster with 148, A266. Transforms II, V, CJB-28.
160
Order 27, reduced side 920
407
513
177230
85 107139
182 I 5363 1 41 124
4368 ~O~ 59
88
283225 200 212
Code: (513,407)(177,230)(182, 139,85, 107)(124,53)(63,22)(41,88) (283)(43,68,28)(19,26,59)(40,7)(33)(225)(212)(200)
Elements: 7,19,22,26,28,33,40,41,43,53,59,63,68,85,88,107, 124,139,177,182,200,21~,225,230,283,407,513
Remarks: In cluster with A318. Transform 1.
]61
CJB
Order 27, reduced side 920
396
524
176220
79129 146 43
170
~~ 13389
35 131112
71 4299
250215
155 173127
AJWD
Code: (524,396)(176,220)(170,129,146,79)(43,133)(67, 12)(55)(89, 131)(112,17)(250,35)(99,71)(215,42)(173)(28,155)(127)
Elements: 12,17,28,35,42,43,55,67,71,79,89,99,112,127,129, 131,133,146,155,170,173,176,215,220,250,396,524
162
Order 27, reduced side 924
267 284
373
250
146 301
227
81 65 67
183
116 105
196
85 95324
224 45 49
139 14394
AJWD
Code: (373,267,284)(250,17)(301)(227, 146)(67, 183)(81,65)(16, 116)(105,196)(324)(10,95)(224,85)(4,49,143)(139,45)(94)
Elements: 4,10,16,17,45,49,65,67,81,85,94,95,105,116,139, 143,146,183,196,224,227,250,267,284,301,324,373
163
Order 27, reduced side 927
419
508
182237
168 148192
55
127
9772
91 7780
112
321 61 78271
I 174199
11586 82
CJB
Code: (508,419)(237,182)(192, 168,148)(55,127)(97,271,72)(91,77) (112,80)(199)(174)(13,78)(32,61)(115,29)(86,4)(82)
Elements: 4,13,29,32,55,61,72,77,78,80,82,86,91,97,112,115, 127,148,168,174,182,192,199,237,271,419,508
Remarks: In cluster with A347. Transform II.
164
Order 27, reduced side 928
395
533
163
232
140 144 69119
224
~8436 32
n 160 68 301
251
171
94 111
JDSII
Code: (533,395) (163, 232) (224,140,144,25) (119, 69) (301) (84, 40,16) (12,251) (28)(36,4)(32)(68) (171, 77, 60) (17, 111)(94)
Elements: 4,12,16,17,25,28,32,36,40,60,68,69,77,84,94,111, 119,140,144,163,171,224,232,251,301,395,533
165
Order 27, reduced side 932
449483
3469 J 75
132 13963
81
39257 260
83 1;- 100171
65 62
244192 189 180
127
AJWD
Code: (483,449) (34,132,69,75,139) (257, Z60) (63, 6) (81) (171, 24) (39,100) (83, 22)(61)(244)(192,65)(62,189,9)(180)(127)
Elements: 6,9,22,24,34,39,61,62,63;65,69,75,81,83,100,127, 132,139,171,180,189,192,244,257,260,449,483
166
Order 27, reduced side 938
431
507
137 130164
119
200 188-'-- 116 123
~O~ 69 133 59
33 44
231 243 254210
Code: (507,431)(164,137,130)(200,119,188)(7, 123)(28, 116)(133,30,1)(29)(59)(50,69)(31,19)(44,254)(243,33)(231)(210)
Elements: 1,7, 19,28,29,30,31,33,44,50,59,69, 116, 119,123, 130, 133, 137, 164, 188,200,210,231,243,254,431,507
Remarks: In cluster with 155, 194, A277, A346.
167
CJB
Order 27, reduced side 939
428
511
83 107
238
159 170 131241
5996g 100 89 81
54 43 136 273
187 169 177133
CJB
Code: (511,428) (83,107,238) (241,159,170,24) (131) (96, 273) (59, 100) (89,81) (34,25)(187,54)(9,16)(177)(43)(36,169)(133)
Elements: 9,16,24,25,34,36,43,54,59,81,83,89,96,100,107, 131,133,159,169,170,177,187,238,241,273,428,511
Remarks: In cluster with SPSR 25:428x856. Transform VIII.
168
Order 27, reduced side 945
446499
194146 153 252
200
54162~9 63131 r--
14468
109
247246
149 174129
Code: (499,446) (194,252) (200, 146, 153) (131,63) (54, 62, 23, 7) (16, 144) (39) (5,247)(246,8)(68)(109)(25,174)(20,149)(129)
Elements: 5,7,8,16,20,23,25,39,54,62,63,68, 109, 129, 131, 144, 146,149,153,174,194,200,246,247,252,446,499
Remarks: In cluster with 185, A400, A427. Transforms I, lb, II, III, IV, V.
169
CJB
Order 27, reduced side 945
440
505
65110
45
151 265197 177
155
46105
79 98 75~36
243'44l 69
240184 165
113
Code: (505,440)(65, 110,265)(197,151,177,45)(155)(46,105) (79, 98) (243)(75,47,58,240)(36,11)(184)(69)(165,8)(44)(113)
Elements: 8,11,36,44,45,46,47,58,65,69,75,79,98,105,110,113, 151,155,165,177,184,197,240,243,265,440,505
Remarks: In cluster with SPSR 25:440x880. Transform VIII.
170
CJB
Order 27, reduced side 948
486 462
134 129 153
247 285
113f-4~ 73
183
1205590 t-- 84
35 33215 201
125 140 150117
AJWD
Code: (486,462) (24,153,285) (247,134,129) (26, 73,183) (113, 21) (47) (120) (215,90,55)(84,201)(35,20)(150,33)(140)(125)(117)
Elements: 20,21,24,26,33,35,47,55,73,84,90,113,117,120, 125, 129,134,140,150,153,183,201,215,247,285,462,486
171
Order 27, reduced side 953
457496
7334
180 204
194 107
268
147 140 8072 124
122f---
f--- 36 4450
79
189 169 176 168141
110
AJWD
Code: (496,457)(73,180,204)(268,194,34) (107)(147, 140)(80,124) (122,72)(36,44)(50,22)(189,79)(176)(169)(168)(31,141)(110)
Elements: 22,31,34,36,44,50,72,73,79,80,107,110,122,124, 140,141,147,168,169,176,180,189,194,204,268,457,496
172
Order 27, reduced side 955
439
516
I
141 150 148
115
191 4868 I210 93 66 8084
42 4576
104 92
282229 248
196
AJWD
Code: (516,439)(141,150,148)(210, 191, 115)(48,93)(68,80)(84,66) (3,45)(76,42)(18,104,12)(92)(282)(19,248)(229)(196)
Elements: 3, 12, 18, 19,42,45,48,66,68, 76, 80, 84, 92,93, 104, 115, 141, 148, 150, 191,196,210,229,248,282,439,516
173
Order 27, reduced side 955
422
533
77125
134143 22042r 35
127 6795
65183 198
56 71 134
45
313
239 224179
CJB
Code: (533,422) (77,125,220) (34, 43) (183,127,198,42,17) (8, 35) (30,95) (25) (67)(65)(134,313)(56,71)(239)(224,45)(179)
Elements: 8,17,25,30,34,35,42,43,45,56,65,67,71,77,95,125, 127,134,179,183,198,220,224,239,313,422,533
Remarks: In cluster with SPSR 25:422x844. Transform VIIIa.
174
Order 27, reduced side 956
144178
25434
380 110
212125
239
128 114
22325252 ~~ 44
59~ 120
17472
115
324 343289
JDSII
Code: (380,254,144,178)(110,34)(212)(239,125)(114,11)(252, 128) (223)(59,174,120)(52,32,44)(20,12)(115)(72)(343)(324)(289)
Elements: 11, 12,20,32,34,44,52,59,72, 110, 114, 115, 120, 125, 128, 144, 174,178,212,223,239,252,254,289,324,343,380
Remarks: In cluster with C150. Transform I.
175
Order 27, reduced side 960
492 468
127178 163
240 252 51 76
56 I40
I 123146 83
48 116
228 216 206168 142
Code: (492,468) (178, 127, 163) (240, 252) (51, 76) (40, 123) (146, 56, 27) (2,31,83)(29)(116)(228,12)(216,48)(206)(168,26)(142)
Elements: 2, 12,26,27,29,31,40,48,51,56,76,83, 116, 123, 127, 142, 146, 163, 168, 178,206,216,228,240,252,468,492
Remarks: in cluster with 208, A422. Transforms I, III, V.
176
CJB
Order 27, reduced side 960
464496
87 99148 130
124
196 176 61 ~0154
72 52 6094 161149
50 44
268 288
199 205
CJB
Code: (496,464)(148,87,99,130)(196,124,176)(61, 26)(14,54, 31) (40)(161)(60,149)(94)(72,52)(288)(268)(50,44)(205)(199)
Elements: 14,26,31,40,44,50,52,54,60,61,72,87,94,99,124, 130,148,149,161,176,196,199,205,268,288,464,496
Remarks: In cluster with 153, A370. Transforms I, IlIa, V.
177
Order 27, reduced side 960
436
524
196240
131
212181
44
8150
15246 38
68~
7969 54
66 55 284224
155 176121
Code: (524,436) (196, 240) (212,131,181) (152, 44) (81, 50) (284) (46, 38,68,79) (224,69)(8,30)(54)(32,66)(55,176)(155)(121)
Elements: 8,30,32,38,44,46,50,54,55,66,68,69,79,81,121,131, 152,155,176,181,196,212,224,240,284,436,524
Remarks: In cluster with 179, A414, A415. Transforms I, I, CJB-24, CJB-25, CJB-26, CJB27.
178
CJB
Order 27, reduced side 960
436
524
196240
139173
21244
73 66I 152
54Ur--
8761 68
38 46
50 63 284224
163 176113
Code: (524,436)(196,240)(212, 139,173)(152,44)(73,66)(284)(32,54,87)(68,30)(224,61)(8,46)(38)(63,176)(163,50)(113)
Elements: 8,30,32,38,44,46,50,54,61,63,66,68,73,87,113,139, 152,163, 173, 176,196,212,224,240,284,436,524
Remarks: In cluster with 178, A414, A415. Transforms I, I, CJB-24, CJB-25, CJB-26, CJB27.
179
CJB
Order 27, reduced side 964
429
535
188241
76132
~140
18753
55 M 13581 73 77
294242
216 212
Code: (535,429) (188, 241) (187, 132, 76, 140) (33,43) (135, 53) (23, 10) (32,21) (55,81,19)(294)(11,73,77)(62)(242)(216)(212)
CJB
Elements: 10,11,19,21,23,32,33;43,53,55,62,73,76,77,81,132, 135,140,187,188,212,216,241,242,294,429,535
Remarks: In cluster with A369. Transform I.
180
Order 27, reduced side 965
277
355 333
78 75 56 68
hJ7 -I-J...=..:-
70 73 55 80109
39
257 321
148 239
52
353301 311
AJWD
Code: (355,277,333) (78, 75, 56, 68) (19,37) (12, 321) (80) (3, 73, 18) (257, 109, 70)(55)(39,239)(148)(353,52)(10,311)(301)
Elements: 3,10,12,18,19,37,39,52,55,56,68,70,73,75,78,80, 109,148,239,257,277,301,311,321,333,353,355
181
Order 27, reduced side 966
261
354 351
90
171
64111 I---
190 164 47
266
158188
6539 99
151 54 50
58 62
349 346
271
AJWD
Cod~ (354,351,261)(90,171) (266,111,64)(190,164)(47,17) (188) (158)(65,99)(151,39)(54,50)(16,349)(346)(4,62)(58)(271)
Elements: 4, 16, 17,39,47,50,54,58; 62, 64, 65, 90, 99, 111, 151, 158, 164, 171, 188, 190,261,266,271,346,349,351,354
Remarks: In cluster with C163, C165. Transforms II, lIe, CJB-32.
182
Order 27, reduced side 970
274336
360
71
,--
70 1 41 1 56 203
I68
99~
312288 60
211159
150 12888
322282
172 194
JDSII
Code: (336,360,274) (71, 203) (312, 24) (15,56) (288, 70, 41) (29, 68) (99) (60,8) (211)(159)(322,150,128)(88,282)(22,194)(172)
Elements: 8,15,22,24,29,41,56,60,68,70,71,88,99,128,150,159, 172,194,203,211,274,282,288,312,322,336,360
183
Order 27, reduced side 970
274336 360
73
,.----
o l39J 60 2017 I r'----
68
312 101288 56
213157
150 12888
322282
172 194
AJWD
Code: (336,360,274) (73, 201) (312, 24) (13, 60) (288, 70, 39) (31, 8) (68) (101) (56,213)(157)(322,150,128)(88,282)(22,194)(172)
Elements: 8,13,22,24,31,.39,56,60,68,70,73,88,101,128,150,157, 172,194,201,213,274,282,288,312,322,336,360
184
Order 27, reduced side 970
446
524
194252
129 149
24663
109 131
144 68
54162~272
200 199146 153
Code: (524,446) (252,194) (246,129,149) (63,131) (109, 20) (144, 25) (272,5) (68) (8,62,39) (200, 54) (199) (23,16) (7, 153) (146)
Elements: 5, 7, 8, 16,20,23,25,39,54,62,63,68, 109, 129, 131, 144, 146, 149, 153, 194,199,200,246,252,272,446,524
Remarks: In cluster with 169, A400, A427. Transforms I, Ib, II, III, IV, V.
185
CJB
Order 27, reduced side 972
436
536
185251
128
211 19770
69 I 115
13792 117 13450 47 68
225 239189 168 151
AJWD
Code: (536,436) (185, 251) (211, 197, 128) (70, 115) (69, 32, 27) (117, 134) (5, 92) (37)(14,239,50) (47, 68) (225) (189) (168,17) (151)
Elements: 5,14,17,27,32,37,47,50,68,69,70,92,115,117,128, 134,151,168,185,189,197,211,225,239,251,436,536
186
Order 27, reduced side 975
113159
268 67 146
435 88184
75119
162
43 120 13976
195 200245 1n 158
50
345 335295
JOSH
Code: (435,268,113,159)(67,46)(21,184)(88)(162,119, 75)(120,139) (43,76)(5,200)(245,195)(177,19)(158)(50,345)(335)(295)
Elements: 5,19,21,43,46,50,67,75,76,88,113,119,120,139,158, 159,162,177,184,195,200,245,268,295,335,345,435
Remarks: In cluster with 193, C145. Transforms I, la, IV.
187
Order 27, reduced side 975
435
540
190245
168 140
232 55
135
37 65 8064 67
69 ~51-46 10245 - 295
203 215
134 128
CJB
Code: (540,435)(245, 190)(232, 168, 140)(55, 135)(65,295,80)(64,67, 37)(102)(215)(203,69,24)(21,46)(45)(20,26)(134)(128)
Elements: 20,21,24,26,37,45,46,55,64,65,67,69,80,102,128, 134,135,140,168,190,203,215,232,245,295,435,540
Remarks: In cluster with A387. Transfonn II.
188
Order 27, reduced side 975
435
540
190245
164 140
236 55
13541 65 80
*57 45 58 106295
199 215142 124
Code: (540,435) (245,190) (236,164,140) (55,135) (65, 295, 80) (52, 71, 41) (106) (20,32)(215)(13,58)(199,57)(45)(142,18)(124)
Elements: 13,18,20,32,41,45,52,55,57,58,65,71,80,106,124, 135,140,142,164,190,199,215,236,245,295,435,540
Remarks: In cluster with A388. Transform II.
189
CJB
Order 27, reduced side 976
471505
34
164138 130
273271
146 136 150
41
71 58106 118
200232
191129 '--
81 5687
AJWD
Code: (505,471) (34, 164,273) (271, 138, 130) (8, 136, 150) (146) (41, 232) (18, 118)(200,71) (191) (58,106) (129) (31,87) (81, 25) (56)
Elements: 8,18,25,31,34,41,56,58,71,81,87,106,118,129,130, 136,138,146,150,164,191,200,232,271,273,471,505
190
Order 27, reduced side 979
298342 339
41
105 96141
257
3678 87
380
177135 98
189
91
70 95
319
235 260
165
AJWD
Code: (342,298,339) (257, 41) (380) (141, 105.96) (9, 87) (36, 78) (177) (135,30) (98,189)(7,91)(319)(25,95,260)(235,70)(165)
Elements: 7,9,25,30,36,41,70,78,87,91,95,96,98,105,135,141, 165, 177, 189,235,257,260,298,319,339,342,380
191
Order 27, reduced side 980
254294
432
40
160214
174
~118
71 88 97222 181
203
104 85 79106
326 345309
AJWD
Code: (432,294,254) (40,214) (160,174) (222,118,47,23,22) (1,181) (24) (88,97,203)(71)(104,85)(79,9)(106)(345)(326)(309)
Elements: 1,9,22,23,24,40,47,71,79,85,88,97,104,106,118, 160,174,181,203,214,222,254,294,309,326,345,432
192
Order 27, reduced side 980
113159
268 67 146
440 88184
75119
162
43 120 13976
195 205245 177 158
50
345 340295
JDSII
Code: (440,268,113,159) (67, 46)(21,184)(88)(162, 119,75) (120, 139) (43,76)(205)(245,195)(177,19)(158)(50,345,5)(340)(295)
Elements: 5, 19,21,43,46,50,67,75,76,88, 113, 119, 120, 139, 158, 159, 162, 177, 184,195,205,245,268,295,340,345,440
Remarks: In cluster with 187, C145. Transforms I, Ib, IV.
193
Order 27, reduced side 982
,431
551
137 130164
44
1191---'- 116 123
200 188 59
~O~ 69177
33
298
231 243210 ,
Code: (551,431) (164,137,130) (200,119,188,44) (7,123) (28,116) (177,30,1) (29)(59)(50,69)(298)(31,19)(243,33)(231)(210)
Elements: 1,7,19,28,29,30,31,33,44,50,59,69,116,119,123,130, 137,164,177,188,200,210,231,243,298,431,551
Remarks: In cluster with 155, 167, A277, A346.
194
CJB
Order 27, reduced side 984
433
551
187246
108 115 114
214 59
~ 83r- 128
101 94 -34
305
219 224 236
CJB
Code: (551,433) (187, 246) (214,108, 115, 114) (128,59) (101, 7) (1, 30, 83) (94, 29)(305)(31,28)(3,25)(34)(236)(5,224)(219)
Elements: 1,3,5,7,25,28,29,30,31,34,59,83,94,101,108,114, 115,128,187,214,219,224,236,246,305,433,551
Remarks: In cluster with A365. Transform I.
195
Order 27, reduced side 985
459
526
109 131
93 219
87 65223 210 36 88
57~~
60 48 137
56
307
236 249193
AJWD
Code: (526,459) (109,131,219) (223, 210, 93) (87, 22) (65, 88) (57,36) (18,33,137) (3,15)(60)(307)(48)(13,249,56)(236)(193)
Elements: 3,13,15,18,22,33,36,48,56,57,60,65,87,88,93,109, 131,137,193,210,219,223,236,249,307,459,526
196
Order 27, reduced side 985
435
550
115
320
182238 245
56 I 58 68
44 9050
81 ~r-- 7335 39
230197 190
116 112140
AJWD
Code: (550,435)(115,320)(238, 182,245) (56, 58,68) (90, 230) (]97, 81, 16)(14,44)(5,190,50)(73)(30)(35,39)(140)(1]6)(112)
Elements: 5, 14, 16, 30, 35, 39, 44, 50, 56, 58, 68, 73, 81,90, 112, 115, 116, 140, 182, 190,197,230,238,245,320,435,550
197
Order 27, reduced side 987
459
528
199
132 260164
232
48 53100 --'=1'-- 98 -
38 50 45
156
105
268227 231
122 139
AJWD
Code: (528,459)(199,260)(232, 132, 164)(48,98,53)(100,32)(156,26,14)(12,50)(45,8) (38) (268) (231) (227,105) (17,139) (122)
Elements: 8,12,14,17,26,32,38,45,48,50,53,98,100,105,122, 132,139,156,164,199,227,231,232,260,268,459,528
198
Order 27, reduced side 988
290 314384
94
172
338248 230 81 91
r--71
101
97 158 143151 103
54 43
336
205 216 231
JDSn
Code: (384,290,314) (94, 172,24) (338) (248, 230) (81, 91) (71, 10) (101) (158, 143)(151,97)(2,336)(103)(54,43)(15,231)(216)(205)
Elements: 2,10,15,24,43,54,71,81,91,94,97,101,103, ]43,151,158,172,205,216,230,231,248,290,314,336,338,384
199
Order 27, reduced side 990
293 274
423
255
312
161
262 76
603'!J 63
179101
41 I 103
188
99 116
305 282
206 197
AJWD
Code: (423,293,274)(19,255)(312)(262,161) (76,179)(101,60)(34, 63,188,103)(5,29)(41,24)(116)(305,99)(282)(206,9)(197)
Elements: 5,9,19,24,29,34,41,60,63,76,99,101,103,116,161, 179,188,197,206,255,262,274,282,293,305,312,423
Remarks: In cluster with C179. Transform I.
200
Order 27, reduced side 993
432
561
79 108'--~
50245
137143
225 243
39 66
104
105
53 ~~ 49 40 316
207 189136 145
Code: (561,432)(79,108,245)(50,29)(137)(225,243, 143)(66,316) (104,39)(105)(207,18)(189,53,19)(15,49,40)(34)(145)(136)
Elements: 15,18,19,29,34,39,40,49,50,53,66,79,104,105,108, 136,137,143,145,189,207,225,243,245,316,432,561
Remarks: In cluster with SPSR 25:432x864. Transform VIlI.
201
cm
Order 27, reduced side 1000
253308
439
93
64 160
131 113 r-- ~ 6749
144147
236205 268
79 l=-8958
51
356325 319
JDSII
Code: (439,308,253) (93,160) (131,113,64) (26, 67) (49, 41) (268) (18, 144) (236,147,205)(79,65)(89,58)(14,51)(356)(325)(319)
Elements: 14,18,26,41,49,51,58,64,65,67,79,89,93,113,131, 144,147,160,205,236,253,268,308,319,325,356,439
202
Order 27, reduced side 1004
336 304364
131118 71 173
90190
4267 231
141 16062
/------r 215195 ~
9788
409
283 312
JDSII
Code: (336,364,304)(131,173)(190, 118,28)(90,231,71)(160,42)(67,141)(215)(5,62)(195)(50,12)(38,409,97)(88)(312)(283)
Elements: 5,12,28,38,42,50,62,67,71,88,90,97,118,131,141, 160,173,190,195,215,231,283,304,312,336,364,409
203
Order 27, reduced side 1004
261
385 358
97164
120134 53
111251 58
115 335
117 57
12972
100
173152
368311
166 159
AJWD
Code: (385,261,358)(164,97)(120,335)(251, 134)(111,53)(58, 115) (117,17)(129,57)(72,100)(368)(173,28)(152,311)(166,7)(159)
Elements: 7,17,28,53,57,58,72,97,100,111,115,117,120,129, 134,152,159,164,166,173,251,261,311,335,358,368,385
204
Order 27, reduced side 1005
275337
393
107168 45
127 15277 91 292
266
~139
88220
125167
147
52 42
346
251199 209
JDSn
Code: (393,275,337) (168, 107) (45,292) (152) (266, 127) (77, 91) (139, 51, 14) (37,220)(88)(125,167)(346,147)(52,251,42)(209)(199)
Elements: 14,37,42,45,51,52,77,88,91,107,125,127,139,147, 152,167,168,199,209,220,251,266,275,292,337,346,393
205
Order 27, reduced side 1008
280324
404
124156
111
213
110221
18927538
80 f--L...-
68 17554 ~'--
52 69
383329
296
AJWD
Code: (404,280,324) (124,156) (111, 213) (275, 221,32) (1,110) (189) (38,175) (80,30)(68)(54,383,35,18)(17,69)(52)(329)(296)
Elements: 1,17,18,30,32,35,38,52,54,68,69,80,110,111,124, 156,175,189,213,221,275,280,296,324,329,383,404
206
Order 27, reduced side 1008
272332
404
60
78 212
162 152
84147
251 57
165189 199
204 34
100 131151 97
51
325
253 228202
JDSH
Code: (404,332,272)(60,212)(78,162,152)(251,147,6)(84)(199, 165) (57, 189)(204)(34,131)(151,100)(325,97)(51,253)(228)(202)
Elements: 6,34,51,57,60,78,84,97,100,131,147,151,152,162, 165,189,199,202,204,212,228,251,253,272,325,332,404
207
Order 27, reduced side 1008
516 492
142 168206 240 252
116 48
83 146123 I 56
40 I76 51
276 264
163 178127
AJWD
Code: (516,492)(240,252) (206,142,168)(116,26)(146,48) (123,83) (276,12)(264)(31,29,56)(2,27)(40,76)(51,178)(163)(127)
Elements: 2,12,26,27,29,31,40,48,51,56,76,83,116,123,127, 142, 146, 163, 168, 178,206,240,252,264,276,492,516
Remarks: In cluster with 176, A422. Transforms I, III, V.
208
Order 27, reduced side 1020 JDSII
298 320
402
104172 107
43 23564
~.L...--
22553 69
281 157
67 55 60
56 175115
393337
290
Code: (402,298,320) (104,172,22) (107, 235) (281, 225) (43, 64) (157, 37,21) (16, 69)(53)(60,175)(67,55)(115)(56,393)(337)(290)
Elements: 16,21,22,37,43,53,55,56,60,64,67,69,104,107,115, 157,172,175,225,235,281,290,298,320,337,393,402
209
Order 27, reduced side 1021
284 308
429
260
332155
27476 88 9636
I....--119
~~ 631
83 55
158 164
381318
160 162
JDSII
Code: (429,284,308)(260,24)(332)(274,155)(76, 88,96)(119, 36)(83,29)(17,63,8) (55, 381) (46) (164) (318,158) (2,162) (160)
Elements: 2,8,17,24,29,36,46,55,63,76,83,88,96,119,155,158, 160,162,164,260,274,284,308,318,332,381,429
210
Order 27, reduced side 1022
461
561
182
279
166 167228 85 97
5783 ~~109 106 94
52 43
78 55282
233186 188
133
AJWD
Code: (561,461) (182, 279) (228,166,167) (85, 97) (57,109) (83, 63, 106) (94,282) (5,52)(233)(20,43)(25,78)(55,188)(186)(133)
Elements: 5,20,25,43,52,55,57,63, 78,83,85,94,97, 106, 109, 133, ]66,167, 182, 186,188,228,233,279,282,461,561
211
Order 27, reduced side 1023
433
590
224 209
117 90148 41 56
235I 153
55186 113 160 97
124
37
198 230 206 228161
JDSII
Code: (590,433)(224,209)(235,148, 117,90)(56,153)(23,160,41) (113) (97)(31, 86)(124,55)(230,24)(22,228)(206)(198,37)(161)
Elements: 22,23,24,31,37,41,55,56,86,90,97, 113, 117, 124, 148, 153, 160, 161, 198,206,209,224,228,230,235,433,590
212
Order 27, reduced side 1028
267
351410
84
183
148
165 58287
125 t---245 67
139
63132
16252 99
193154
390
291
180 167
AJWD
Code: (410,267,351) (183,84) (148, 287) (245, 165) (125, 58) (9, 139) (67) (132, 162,63)(99,390)(193,52)(154,30)(291)(180,13)(167)
Elements: 9,13,30,52,58,63,67,84,99,125,132,139,148,154, 162,165,167,180,183,193,245,267,287,291,351,390,410
213
Order 27, reduced side 1032
272
356404
89
183
9451
10150
252 351
151 278
59
164 ~180 ~64
299 325
196 212
JDSII
Code: (404,272,356) (183,89) (5,351) (94) (252,101,51) (50,278) (151) (180,164,59)(26,325)(41,18)(23,299)(64)(16,212)(196)
Elements: 5, 16, 18,23,26,41,50,51,59,64,89,94, 101,151, 164,180, 183, 196,212,252,272,278,299,325,351,356,404
214
Order 27, reduced side 1038
331 313
394
63
286 295170
287
53117
64 94100
175 201111 79
115 1--.-
40 51
357
246 229206
AJWD
Code: (394,331,313) (18, 295) (63, 286) (287,170) (117,53) (94, 201) (64,175,100)(357,111)(15,79)(115)(51,28)(246,40)(229)(206)
Elements: 15,18,28,40,51,53,63,64,79,94,100,111,115,117, 170, 175,201,206,229,246,286,287,295,313,331,357,394
215
Order 27, reduced side 1040
500540
120 12796
253236 208 6197 73
112 r-r-r-r-1
5352
126 ~71
264 292 287
197
JDSU
Code: (540,500) (120, 127,253) (236, 208, 96) (16,97,7) (61, 73) (112) (29,32) (20, 53)(126)(52)(28,292)(19,287)(71)(264)(197)
Elements: 7, 16, 19,20,28,29,32,52,53,61, 71, 73, 96, 97, 112, 120, 126, 127, 197,208,236,253,264,287,292,500,540
216
Order 27, reduced side 1050
302
381 367
79 89134
143
70 ;-164
84 r;;109
296 324
132 111
187
7655
373 359318
AJWD
Code: (381,302,367)(79,134,89)(43,324)(296, 164)(70, 19)(62)(109,25)(84,11)(73)(132,187,111)(76,35)(373,55)(359)(318)
Elements: 11,19,25,35,43,55,62,70,73,76,79,84,89,109,111, 132,134,164,187,296,302,318,324,359,367,373,381
217
Order 27, reduced side 1050
269
367414
98171
73
197 195141
273 244
-Tl 53132 122
165114
42
363 366321
JDSII
Code: (414,367,269) (98,171) (197,195,73) (273,141) (244) (132, 9) (20,53,122) (165,23,18)(5,33)(28)(114)(366)(363,42)(321)
Elements: 5,9,18,20,23,28,33,42,53,73,98,114,122,132,141, 165,171,195,197,244,269,273,321,363,366,367,414
218
Order 27, reduced side 1060
491
569
226139
265164
266I 43 39
46 1 71 IT:;143 ~ 153
124 7041
304
225184 157
190
AJWD
Code: (569,491)(226,265)(266,164,139)(25, 71,43)(34,153,39)(143,46)(28,49)(304)(124,21)(70)(225,41)(33,190)(184)(157)
Elements: 21,25,28,33,34,39,41,43,46,49,70,71,124, ]39, 143,153,157,164,184,190,225,226,265,266,304,491,569
219
Order 27, reduced side 1064
266
416382
150116
151185
159
256 313
128167 200
7072
18682
130
148369
297
206 192
JDSII
Code: (416,266,382)(150,116)(185,313)(256,159, 151)(8,200, 128) (167)(186,70)(72,369)(82,130,25)(297)(34,48)(206,14)(192)
Elements: 8,14,25,34,48,70,72,82,116,128,130,150,151,159, 167,185,186,192,200,206,256,266,297,313,369,382,416
220
Order 27, reduced side 1064
500564
198134
173 302
257
8256 l- 106
84 I---l-144
92 38 4079 6898
47
243 262192 222
145
AJWD
Code: (564,500)(198,302)(257,173,134)(82, 106, 144)(84,56,33)(23, 10)(92)(79)(40,262)(68,38)(243,98)(222)(47,192)(145)
Elements: 10,23,33,38,40,47,56,68,79,82,84,92,98,106,134,144, 145,173,192,198,222,243,257,262,302,500,564
221
Order 27, reduced side 1075
278
379418
140 138
37
71 148 50170 172
f.------l-. 125165 75
94274
109 192 176 174150
383350342
AJWD
Code: (418,278,379) (140,138) (37,170,172) (50,125) (274,165,71,48) (23,75) (94)(192,8) (176, 2) (174) (109,150) (383) (350) (342)
Elements: 2,8,23,37,48,50, 71, 75, 94, 109, 125,138, 140, 150, 165, 170, 172, 174, 176,192,274,278,342,350,379,383,418
222
Order 27, reduced side 1085
325 328
432
107~
102165 64
21562
10444
241298 183
139
224
5794
412355
318
JDSII
Code: (432,325,328)(107,165,39, 14)(11,102,215)(25)(64)(62,2) (104)(298,241)(183,44)(139,9)(224)(57,412,94)(355)(318)
Elements: 2,9,11,14,25,39,44,57,62,64,94,102,104,107,139, 165,183,215,224,241,298,318,325,328,355,412,432
223
Order 27, reduced side 1091
310 335
446
92
cr;- 193
53~141 360
88 84262 156
121192
120
383 396
312
AJWD
Code: (446,310,335)(92, 193,25)(360)(34,58)(10,24)(262, 141,53) (39,43)(88,4)(84,156)(121,192)(120,36)(396)(383)(312)
Elements: 4, 10,24,25,34,36,39,43,53,58,84,88,92, 120,121,141, 156,192, 193,262,310,312,335,360,383,396,446
224
Order 27, reduced side 1111
324 340
447
123185
119149 35657
128302
93 ~71
105
59
60 106140
88
415362
334
AJWD
Code: (447,324,340)(123,185,16)(356)(302,149, 119)(57, 128)(105,71)(93,56)(140,59)(37,19)(18,106)(60,88)(415)(362)(334)
Elements: 16, 18, 19, 37, 56, 57, 59, 60, 71, 88, 93, 105, 106, 119, 123, 128, 140, 149, 185,302,324,334,340,356,362,415,447
225
Order 27, reduced side 1123
302367
454
88 65
~149
84
151
140
165204 348128
278
113 60180
144
391 408
324
JDSII
Code: (454, 302, 367) (88, 149,65) (84, 348) (38, 50) (26, 12) (51, 11) (40, 204) (278,165,37)(128)(113,180)(144,60)(408)(391)(324)
Elements: 11,12,26,37,38,40,50,51,60,65,84,88,113,128,144, 149,165,180,204,278,302,324,348,367,391,408,454
226
Order 27, reduced side 1143
308343
492
273
88 378148
256 60 ~'-55 106
77~140
108
130100 96
395 422
326
JDSn
Code: (492,308,343)(273,35)(378)(256,148,88)(60,28)(27, 106,140) (55)(108,77,23)(54,24)(130)(31,100)(96,422)(395)(326)
Elements: 23,24,27,28,31,35,54,55,60,77,88,96,100,106,108, 130,140,148,256,273,308,326,343,378,395,422,492
227