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Orthogonal Array ListsWarren F. Kuhfeld - SAS
This report provides a list of virtually all known strength-two orthogonal arrays up through 143 runs1
(rows or factor combinations) and a list of additional orthogonal arrays up through 1,000 runs. At the end of these lists is a reference list of books and papers on orthogonal array construction. The reference list mostly covers newer and larger arrays. Many of the older arrays were created based on secondary sources such as Orthogonal Fractional Factorial Designs by Dey (1985); Orthogonal Arrays by Hedayat, Sloane, and Stufken (1999); and A Library of Orthogonal Arrays, by Sloane (2005). Their reference lists are not duplicated here. The work so far could not have happened without the work of many people over the span of over 110 years (the earliest reference in this list is an 1893 paper by the French mathematician Jacques Hadamard). This resource cannot continue to grow without your help. Thanks to Don Anderson, StatDesign; Warwick de Launey, Center for Communications Research; Nam-Ky Nguyen, Gendex; Shanqi Pang, Henan Normal University; Neil Sloane, AT&T Shannon Lab; Chung-yi Suen, Cleveland State University; Randy Tobias, SAS Institute Inc.; Ian Wakeling, Qi Statistics; J. C. Wang, Western Michigan University; and Yingshan Zhang, Henan Normal University, who have all kindly helped with some of the arrays in this catalog.
While the orthogonal array lists are virtually complete for the smaller arrays, new arrays are being discovered all the time. The goal is to create the most complete strength-two orthogonal array source ever assembled and to provide computerized tools that completely automate their construction.
The first listing presents strength-two orthogonal arrays up through 143 runs. The columns include the number or runs, the array, and the lineage or rules for making the array. The listing is sorted by the number of runs. Within runs, it is sorted by the number of two-level factors, then the number of three-level factors, and so on, all in descending order. Hence within runs, the arrays with the most two-level factors are listed first. The second column after the number of runs contains a running count of the number of arrays that can be made for this number of runs. The first array is 23, which has 3 two-level factors in 4 runs. Further down the list you see 2137, which has 1 two-level factor and 7 three-level factors in 18 runs. The base is the number of levels and the exponent is the number of factors. Hence, 2137 means a 2 � 3 � 3 � 3 � 3 � 3 � 3 � 3 design. All of these arrays are strength-two main-effects designs, which means that all level pairs occur equally often within every pair of columns.
The lineage of an array shows how it can be made from other arrays. Some arrays have no lineage. These arrays are called parent arrays. They are constructed in many different ways�some with simple algebra, some with very complicated algebra, and others through computerized searches. The remaining arrays are constructed from the parents. For example, the array 27 has a lineage of 2441; 41 ! 23, which means it can be made from 2441 by replacing 41 with copies of the array 23 in 4 runs. The first part of the lineage gives the parent array, which will always have the same number of runs as the array of interest. Subsequent parts of the lineage show how to replace one or more factors in the parent with copies of smaller arrays that appear before this array in the listing. The replacement array appears after the arrow (for example, the 23 in 41 ! 23). The factor that
1There are a few missing designs in 108 runs. I would welcome help in making them.
needs to be replaced appears before the arrow, and it also gives the number of runs in the replacementarray. The exponent on this factor will always be 1. Some replacements, particularly for four-levelfactors, might occur more than once. The lineage provides information on what to do. The numberof times it needs to happen is not explicitly stated in this listing, but it is obvious from the context.Consider, for example, the array 215 whose lineage consists of 45; 41 ! 23. 41 must be replaced by23 a total of 5 times. The lineage does not consist of something like 45; 45 ! 215 because thatwould hide the critical information that it is the array 23 that is needed to make the larger array. Thearray 45 becomes 2344 after the first replacement. This array has too many four-level factors andnot enough two-level factors, so 2344 becomes 2643, which becomes 2942, which becomes 21241,which finally, after the last replacement, becomes 215, the desired result.
Replacing a four-level factor by 3 two-level factors consists of replacing: a 0 in the four-level factorby the first row of the 23 array, a 1 in the four-level factor by the second row of 23, and so on. Moregenerally, to replace a p-level factor by an array in p runs, replace level i D 0; :::; p � 1 with rowi C 1 of the array in p runs. The following example illustrates:
2441; n D 8
0000 0
0011 2
0101 1
0110 3
1001 3
1010 1
1100 2
1111 0
and 23; n D 4
000
011
101
110
makes 27; n D 8
0000 000
0011 101
0101 011
0110 110
1001 110
1010 011
1100 101
1111 000
where 41 ! 23
0 ! 000
1 ! 011
2 ! 101
3 ! 110
In practice, you never have to actually do any of this because the SAS macro %MktEx does it all foryou. See the Web book Marketing Research Methods in SAS for more information on the %MktExmacro, which automates orthogonal array and nonorthogonal factorial design creation. In particular,see the chapters “Experimental Design and Choice Modeling Macros” and “Discrete Choice” fordocumentation and numerous examples of its use. The book and macros are free on the Web athttp://support.sas.com/techsup/tnote/tnote_stat.html#market.
The following examples show how easy it is to run %MktEx to get orthogonal arrays:
%mktex(2 ** 15, n=16)%mktex(2 3 ** 7, n=18)%mktex(2 ** 18 4 4 8, n=32)
However, %MktEx has many more options because it has many other capabilities, including facilitiesfor making highly restricted designs. While the examples in Marketing Research Methods in SAShave a marketing research orientation, researchers in many other areas use %MktEx to make designsfor a variety of purposes.
When orthogonal arrays are not available, the %MktEx macro automatically constructs a D-efficientnonorthogonal design. For 31525 in 36 runs, %MktEx usually makes a design that is mostlyorthogonal but with a few correlated factors. For 231 in 33 runs (which is an unusual request, sincethere is an orthogonal array in 32 runs), %MktEx makes a design that is nonorthogonal but with allfactors slightly and equally correlated.
%mktex(3 ** 15 2 ** 5, n=36)%mktex(2 ** 31, n=33)
%MktEx can also make designs with interactions and complicated restrictions.
While this listing shows virtually all known orthogonal arrays up to 143 runs, it does not contain allknown lineages for each orthogonal array, nor does it indicate that many orthogonal arrays, includingmany parent arrays, can be made in multiple ways. For example, the array 27 in 8 runs can alterna-tively be constructed as a Hadamard array based on the fact that 8�1 D 7 is prime or based on the factthat 8 D 23. The page http://support.sas.com/techsup/technote/ts723_Designs.txt
provides one orthogonal array for every parent in this listing (except for the full-factorial designs,which require no special expertise to generate). Also see Neil Sloane’s orthogonal array page,http://neilsloane.com/oadir/. Sloane’s page provides many strength two-orthogonalarrays including some arrays that are alternatives to the ones shown here. His page also containsarrays of strength greater than 2, assorted Hadamard matrices constructed in alternative ways, andmany other useful designs not covered here. There is also a link to the official Web page for the 1999book Orthogonal Arrays by Hedayat, Sloane, and Stufken.
Runs Count Design Lineage
4 1 23
6 1 2131
8 1 27 2441; 41 ! 23
8 2 2441
9 1 34
10 1 2151
12 1 211
12 2 2431
12 3 2261
12 4 3141
14 1 2171
15 1 3151
16 1 215 45; 41 ! 23
16 2 21241 45; 41 ! 23
16 3 2942 45; 41 ! 23
16 4 2881
16 5 2643 45; 41 ! 23
16 6 2344 45; 41 ! 23
16 7 45
18 1 2137 3661; 61 ! 2131
18 2 2191
18 3 3661
20 1 219
20 2 2851
20 3 22101
20 4 4151
21 1 3171
22 1 21111
24 1 223 22041; 41 ! 23
24 2 22041
24 3 21631 2133141; 41 ! 23
24 4 21461 2114161; 41 ! 23
24 5 2133141
24 6 212121
24 7 2114161
Runs Count Design Lineage
24 8 3181
25 1 56
26 1 21131
27 1 313 3991; 91 ! 34
27 2 3991
28 1 227
28 2 21271
28 3 22141
28 4 4171
30 1 213151 21151; 151 ! 3151
30 2 21151
30 3 31101
30 4 5161
32 1 231 4881; 81 ! 2441; 41 ! 23
32 2 22841 4881; 81 ! 2441; 41 ! 23
32 3 22542 4881; 81 ! 2441; 41 ! 23
32 4 22481 4881; 41 ! 23
32 5 22243 4881; 81 ! 2441; 41 ! 23
32 6 2214181 4881; 41 ! 23
32 7 21944 4881; 81 ! 2441; 41 ! 23
32 8 2184281 4881; 41 ! 23
32 9 21645 4881; 81 ! 2441; 41 ! 23
32 10 216161
32 11 2154381 4881; 41 ! 23
32 12 21346 4881; 81 ! 2441; 41 ! 23
32 13 2124481 4881; 41 ! 23
32 14 21047 4881; 81 ! 2441; 41 ! 23
32 15 294581 4881; 41 ! 23
32 16 2748 4881; 81 ! 2441; 41 ! 23
32 17 264681 4881; 41 ! 23
32 18 2449 4881; 81 ! 2441
32 19 234781 4881; 41 ! 23
32 20 4881
33 1 31111
34 1 21171
35 1 5171
36 1 235
36 2 22731
Runs Count Design Lineage
36 3 22032
36 4 2183161
36 5 21634 21691; 91 ! 34
36 6 21691
36 7 2133261
36 8 21362
36 9 211312 312121; 121 ! 211
36 10 2103861
36 11 2103162
36 12 293462
36 13 2863
36 14 24313 312121; 121 ! 2431
36 15 243163
36 16 233961
36 17 233263
36 18 2231261 312121; 121 ! 2261
36 19 223562
36 20 22181
36 21 213862 3763; 61 ! 2131
36 22 213363
36 23 31341 312121; 121 ! 3141
36 24 312121
36 25 3763
36 26 4191
38 1 21191
39 1 31131
40 1 239 23641; 41 ! 23
40 2 23641
40 3 22851 2254151; 41 ! 23
40 4 2254151
40 5 222101 21941101; 41 ! 23
40 6 220201
40 7 21941101
40 8 5181
42 1 213171 6171; 61 ! 2131
42 2 21211
42 3 31141
42 4 6171
44 1 243
44 2 216111
44 3 22221
44 4 41111
Runs Count Design Lineage
45 1 31051 39151; 151 ! 3151
45 2 39151
45 3 5191
46 1 21231
48 1 247 412121; 121 ! 211; 41 ! 23
48 2 24441 412121; 121 ! 211; 41 ! 23
48 3 24142 412121; 121 ! 211; 41 ! 23
48 4 24031 412121; 121 ! 2431; 41 ! 23
48 5 24081
48 6 23843 412121; 121 ! 211; 41 ! 23
48 7 23861 412121; 121 ! 2261; 41 ! 23
48 8 2373141 412121; 121 ! 2431; 41 ! 23
48 9 236121 412121; 41 ! 23
48 10 23544 412121; 121 ! 211; 41 ! 23
48 11 2354161 412121; 121 ! 2261; 41 ! 23
48 12 2343142 412121; 121 ! 2431; 41 ! 23
48 13 2333181
48 14 23341121 412121; 41 ! 23
48 15 23245 412121; 121 ! 211; 41 ! 23
48 16 2324261 412121; 121 ! 2261; 41 ! 23
48 17 2313143 412121; 121 ! 2431; 41 ! 23
48 18 2316181
48 19 23042121 412121; 41 ! 23
48 20 22946 412121; 121 ! 211; 41 ! 23
48 21 2294361 412121; 121 ! 2261; 41 ! 23
48 22 2283144 412121; 121 ! 2431; 41 ! 23
48 23 22743121 412121; 41 ! 23
48 24 22647 412121; 121 ! 211; 41 ! 23
48 25 2264461 412121; 121 ! 2261; 41 ! 23
48 26 2253145 412121; 121 ! 2431; 41 ! 23
48 27 22444121 412121; 41 ! 23
48 28 224241
48 29 22348 412121; 121 ! 211; 41 ! 23
48 30 2234561 412121; 121 ! 2261; 41 ! 23
48 31 2223146 412121; 121 ! 2431; 41 ! 23
48 32 22145121 412121; 41 ! 23
48 33 22049 412121; 121 ! 211; 41 ! 23
48 34 2204661 412121; 121 ! 2261; 41 ! 23
48 35 2193147 412121; 121 ! 2431; 41 ! 23
48 36 21846121 412121; 41 ! 23
48 37 217410 412121; 121 ! 211; 41 ! 23
48 38 2174761 412121; 121 ! 2261; 41 ! 23
48 39 2163148 412121; 121 ! 2431; 41 ! 23
48 40 21547121 412121; 41 ! 23
48 41 214411 412121; 121 ! 211; 41 ! 23
48 42 2144861 412121; 121 ! 2261; 41 ! 23
Runs Count Design Lineage
48 43 2133149 412121; 121 ! 2431; 41 ! 23
48 44 21248121 412121; 41 ! 23
48 45 211412 412121; 121 ! 211
48 46 2114961 412121; 121 ! 2261; 41 ! 23
48 47 21031410 412121; 121 ! 2431; 41 ! 23
48 48 2949121 412121; 41 ! 23
48 49 2841061 412121; 121 ! 2261; 41 ! 23
48 50 2731411 412121; 121 ! 2431; 41 ! 23
48 51 26410121 412121; 41 ! 23
48 52 2541161 412121; 121 ! 2261; 41 ! 23
48 53 2431412 412121; 121 ! 2431
48 54 23411121 412121; 41 ! 23
48 55 2241261 412121; 121 ! 2261
48 56 31413 412121; 121 ! 3141
48 57 31161
48 58 412121
49 1 78
50 1 21511 510101; 101 ! 2151
50 2 21251
50 3 510101
51 1 31171
52 1 251
52 2 217131
52 3 22261
52 4 41131
54 1 21325 3206191; 91 ! 34; 61 ! 2131
54 2 2132191 3206191; 61 ! 2131
54 3 21271
54 4 32461 3206191; 91 ! 34
54 5 3206191
54 6 318181
55 1 51111
56 1 255 25241; 41 ! 23
56 2 25241
56 3 24071 2374171; 41 ! 23
56 4 2374171
56 5 230141 22741141; 41 ! 23
56 6 228281
56 7 22741141
56 8 7181
57 1 31191
Runs Count Design Lineage
58 1 21291
60 1 259
60 2 23031
60 3 22461
60 4 22351
60 5 221101
60 6 2183151 218151; 151 ! 3151
60 7 218151
60 8 21631101 21561101; 61 ! 2131
60 9 2165161 21561101; 101 ! 2151
60 10 21561101
60 11 22301
60 12 314151 41151; 151 ! 3151
60 13 31201
60 14 41151
60 15 51121
62 1 21311
63 1 31371 312211; 211 ! 3171
63 2 312211
63 3 7191
64 1 263 416161; 161 ! 45; 41 ! 23
64 2 26041 416161; 161 ! 45; 41 ! 23
64 3 25742 416161; 161 ! 45; 41 ! 23
64 4 25681 2541781; 41 ! 23
64 5 25443 416161; 161 ! 45; 41 ! 23
64 6 2534181 2541781; 41 ! 23
64 7 25144 416161; 161 ! 45; 41 ! 23
64 8 2504281 2541781; 41 ! 23
64 9 24982 41483; 81 ! 2441; 41 ! 23
64 10 24845 416161; 161 ! 45; 41 ! 23
64 11 248161 416161; 41 ! 23
64 12 2474381 2541781; 41 ! 23
64 13 2464182 41483; 81 ! 2441; 41 ! 23
64 14 24546 416161; 161 ! 45; 41 ! 23
64 15 24541161 416161; 41 ! 23
64 16 2444481 2541781; 41 ! 23
64 17 2434282 41483; 81 ! 2441; 41 ! 23
64 18 24247 416161; 161 ! 45; 41 ! 23
64 19 24242161 416161; 41 ! 23
64 20 24283 41483; 41 ! 23
64 21 2414581 2541781; 41 ! 23
64 22 2404382 41483; 81 ! 2441; 41 ! 23
64 23 23948 416161; 161 ! 45; 41 ! 23
64 24 23943161 416161; 41 ! 23
Runs Count Design Lineage
64 25 2394183 41483; 41 ! 23
64 26 2384681 2541781; 41 ! 23
64 27 2374482 41483; 81 ! 2441; 41 ! 23
64 28 23649 416161; 161 ! 45; 41 ! 23
64 29 23644161 416161; 41 ! 23
64 30 2364283 41483; 41 ! 23
64 31 2354781 2541781; 41 ! 23
64 32 23584 2541084; 41 ! 23
64 33 2344582 41483; 81 ! 2441; 41 ! 23
64 34 233410 416161; 161 ! 45; 41 ! 23
64 35 23345161 416161; 41 ! 23
64 36 2334383 41483; 41 ! 23
64 37 2324881 2541781; 41 ! 23
64 38 2324184 2541084; 41 ! 23
64 39 232321
64 40 2314682 41483; 81 ! 2441; 41 ! 23
64 41 230411 416161; 161 ! 45; 41 ! 23
64 42 23046161 416161; 41 ! 23
64 43 2304483 41483; 41 ! 23
64 44 2294981 2541781; 41 ! 23
64 45 2294284 2541084; 41 ! 23
64 46 2284782 41483; 81 ! 2441; 41 ! 23
64 47 22885 4786; 81 ! 2441; 41 ! 23
64 48 227412 416161; 161 ! 45; 41 ! 23
64 49 22747161 416161; 41 ! 23
64 50 2274583 41483; 41 ! 23
64 51 22641081 2541781; 41 ! 23
64 52 2264384 2541084; 41 ! 23
64 53 2254882 41483; 81 ! 2441; 41 ! 23
64 54 2254185 4786; 81 ! 2441; 41 ! 23
64 55 224413 416161; 161 ! 45; 41 ! 23
64 56 22448161 416161; 41 ! 23
64 57 2244683 41483; 41 ! 23
64 58 22341181 2541781; 41 ! 23
64 59 2234484 2541084; 41 ! 23
64 60 2224982 41483; 81 ! 2441; 41 ! 23
64 61 2224285 4786; 81 ! 2441; 41 ! 23
64 62 221414 416161; 161 ! 45; 41 ! 23
64 63 22149161 416161; 41 ! 23
64 64 2214783 41483; 41 ! 23
64 65 22186 4786; 41 ! 23
64 66 22041281 2541781; 41 ! 23
64 67 2204584 2541084; 41 ! 23
64 68 21941082 41483; 81 ! 2441; 41 ! 23
64 69 2194385 4786; 81 ! 2441; 41 ! 23
64 70 218415 416161; 161 ! 45; 41 ! 23
64 71 218410161 416161; 41 ! 23
64 72 2184883 41483; 41 ! 23
Runs Count Design Lineage
64 73 2184186 4786; 41 ! 23
64 74 21741381 2541781; 41 ! 23
64 75 2174684 2541084; 41 ! 23
64 76 21641182 41483; 81 ! 2441; 41 ! 23
64 77 2164485 4786; 81 ! 2441; 41 ! 23
64 78 215416 416161; 161 ! 45; 41 ! 23
64 79 215411161 416161; 41 ! 23
64 80 2154983 41483; 41 ! 23
64 81 2154286 4786; 41 ! 23
64 82 21441481 2541781; 41 ! 23
64 83 2144784 2541084; 41 ! 23
64 84 21487 89; 81 ! 2441; 41 ! 23
64 85 21341282 41483; 81 ! 2441; 41 ! 23
64 86 2134585 4786; 81 ! 2441; 41 ! 23
64 87 212417 416161; 161 ! 45; 41 ! 23
64 88 212412161 416161; 41 ! 23
64 89 21241083 41483; 41 ! 23
64 90 2124386 4786; 41 ! 23
64 91 21141581 2541781; 41 ! 23
64 92 2114884 2541084; 41 ! 23
64 93 2114187 89; 81 ! 2441; 41 ! 23
64 94 21041382 41483; 81 ! 2441; 41 ! 23
64 95 2104685 4786; 81 ! 2441; 41 ! 23
64 96 29418 416161; 161 ! 45; 41 ! 23
64 97 29413161 416161; 41 ! 23
64 98 2941183 41483; 41 ! 23
64 99 294486 4786; 41 ! 23
64 100 2841681 2541781; 41 ! 23
64 101 284984 2541084; 41 ! 23
64 102 284287 89; 81 ! 2441
64 103 2741482 41483; 81 ! 2441; 41 ! 23
64 104 274785 4786; 81 ! 2441; 41 ! 23
64 105 2788 89; 81 ! 2441; 41 ! 23
64 106 26419 416161; 161 ! 45; 41 ! 23
64 107 26414161 416161; 41 ! 23
64 108 2641283 41483; 41 ! 23
64 109 264586 4786; 41 ! 23
64 110 2541781
64 111 2541084
64 112 2441582 41483; 81 ! 2441
64 113 244885 4786; 81 ! 2441
64 114 244188 89; 81 ! 2441
64 115 23420 416161; 161 ! 45; 41 ! 23
64 116 23415161 416161; 41 ! 23
64 117 2341383 41483; 41 ! 23
64 118 234686 4786; 41 ! 23
64 119 421 416161; 161 ! 45
64 120 416161
Runs Count Design Lineage
64 121 41483
64 122 4786
64 123 89
65 1 51131
66 1 2131111 21331; 331 ! 31111
66 2 21331
66 3 31221
66 4 61111
68 1 267
68 2 219171
68 3 22341
68 4 41171
69 1 31231
70 1 215171 21351; 351 ! 5171
70 2 21351
70 3 51141
70 4 71101
72 1 271 26841; 41 ! 23
72 2 26841
72 3 26331 2603141; 41 ! 23
72 4 2603141
72 5 25632 2533241; 41 ! 23
72 6 2543161 251314161; 41 ! 23
72 7 2533241
72 8 25234 2494191; 91 ! 34; 41 ! 23
72 9 25291 2494191; 41 ! 23
72 10 251314161
72 11 2493441 2494191; 91 ! 34
72 12 2493261 246324161; 41 ! 23
72 13 2494191
72 14 24962 2464162; 41 ! 23
72 15 247312 24431241; 41 ! 23
72 16 2463861 243384161; 41 ! 23
72 17 246324161
72 18 2463162 243314162; 41 ! 23
72 19 2464162
72 20 2453462 242344162; 41 ! 23
72 21 24431241
72 22 24463 2414163; 41 ! 23
72 23 243384161
72 24 243314162
72 25 242344162
Runs Count Design Lineage
72 26 2414163
72 27 240313 23731341; 41 ! 23
72 28 2403163 237314163; 41 ! 23
72 29 2393961 236394161; 41 ! 23
72 30 2393263 236324163; 41 ! 23
72 31 23831261 2353124161; 41 ! 23
72 32 2383562 235354162; 41 ! 23
72 33 238181 23541181; 41 ! 23
72 34 23731341
72 35 2373862 234384162; 41 ! 23
72 36 2373363 234334163; 41 ! 23
72 37 237314163
72 38 236312121 236361; 361 ! 312121
72 39 236394161
72 40 2363763 236361; 361 ! 3763
72 41 236324163
72 42 236361
72 43 2353124161
72 44 235354162
72 45 23541181
72 46 234384162
72 47 234334163
72 48 23164
72 49 2303164
72 50 22931162 22731161121; 121 ! 2261
72 51 2283264
72 52 22731161121
72 53 2273664
72 54 223324 324241; 241 ! 22041; 41 ! 23
72 55 22232061 2193204161; 41 ! 23
72 56 22131662 2183164162; 41 ! 23
72 57 22032441 324241; 241 ! 22041
72 58 22031263 2173124163; 41 ! 23
72 59 2193204161
72 60 2193864 215374165; 61 ! 2131; 41 ! 23
72 61 2183164162
72 62 2183765 215374165; 41 ! 23
72 63 2173124163
72 64 2173366 214334166; 41 ! 23
72 65 216325 324241; 241 ! 2133141; 41 ! 23
72 66 216384164 215374165; 61 ! 2131
72 67 21532161 2123214161; 41 ! 23
72 68 215374165
72 69 21432461 324241; 241 ! 2114161; 41 ! 23
72 70 21431762 2113174162; 41 ! 23
72 71 214334166
72 72 21332541 324241; 241 ! 2133141
72 73 21332062 2103204162; 41 ! 23
Runs Count Design Lineage
72 74 21331363 2103134163; 41 ! 23
72 75 212324121 324241; 241 ! 212121
72 76 2123214161
72 77 21231663 293164163; 41 ! 23
72 78 2123964 28384165; 61 ! 2131; 41 ! 23
72 79 2113244161 324241; 241 ! 2114161
72 80 21132061121
72 81 2113174162
72 82 21131264 283124164; 41 ! 23
72 83 2113865 28384165; 41 ! 23
72 84 2103204162
72 85 21031662121
72 86 2103134163
72 87 2103466 27344166; 41 ! 23
72 88 293164163
72 89 2931263121
72 90 29394164 28384165; 61 ! 2131
72 91 293766 26374166; 41 ! 23
72 92 283124164
72 93 28384165
72 94 283864121 273765121; 61 ! 2131
72 95 283367 25334167; 41 ! 23
72 96 273765121
72 97 27344166
72 98 26374166
72 99 263366121
72 100 25334167
72 101 32581 324241; 241 ! 3181
72 102 324241
72 103 8191
74 1 21371
75 1 3159 58151; 151 ! 3151
75 2 31251
75 3 58151
76 1 275
76 2 220191
76 3 22381
76 4 41191
77 1 71111
78 1 2131131 21391; 391 ! 31131
78 2 21391
78 3 31261
78 4 61131
Runs Count Design Lineage
80 1 279 25143201; 201 ! 219; 41 ! 23
80 2 27641 25143201; 201 ! 219; 41 ! 23
80 3 27342 25143201; 201 ! 219; 41 ! 23
80 4 27281
80 5 27043 25143201; 201 ! 219
80 6 26851 25143201; 201 ! 2851; 41 ! 23
80 7 2654151 25143201; 201 ! 2851; 41 ! 23
80 8 2624251 25143201; 201 ! 2851; 41 ! 23
80 9 262101 25143201; 201 ! 22101; 41 ! 23
80 10 2615181
80 11 260201 25143201; 41 ! 23
80 12 2594351 25143201; 201 ! 2851
80 13 25941101 25143201; 201 ! 22101; 41 ! 23
80 14 25741201 25143201; 41 ! 23
80 15 25642101 25143201; 201 ! 22101; 41 ! 23
80 16 25581101
80 17 25442201 25143201; 41 ! 23
80 18 25343101 25143201; 201 ! 22101
80 19 2514451 25143201; 201 ! 4151
80 20 25143201
80 21 240401
80 22 23445 410201; 201 ! 219; 41 ! 23
80 23 23146 410201; 201 ! 219; 41 ! 23
80 24 22847 410201; 201 ! 219; 41 ! 23
80 25 22548 410201; 201 ! 219; 41 ! 23
80 26 2234551 410201; 201 ! 2851; 41 ! 23
80 27 22249 410201; 201 ! 219; 41 ! 23
80 28 2204651 410201; 201 ! 2851; 41 ! 23
80 29 22044101 410201; 201 ! 22101; 41 ! 23
80 30 219410 410201; 201 ! 219
80 31 21844201 410201; 41 ! 23
80 32 2174751 410201; 201 ! 2851; 41 ! 23
80 33 21745101 410201; 201 ! 22101; 41 ! 23
80 34 21545201 410201; 41 ! 23
80 35 2144851 410201; 201 ! 2851; 41 ! 23
80 36 21446101 410201; 201 ! 22101; 41 ! 23
80 37 21246201 410201; 41 ! 23
80 38 2114951 410201; 201 ! 2851; 41 ! 23
80 39 21147101 410201; 201 ! 22101; 41 ! 23
80 40 2947201 410201; 41 ! 23
80 41 2841051 410201; 201 ! 2851
80 42 2848101 410201; 201 ! 22101; 41 ! 23
80 43 2648201 410201; 41 ! 23
80 44 2549101 410201; 201 ! 22101; 41 ! 23
80 45 2349201 410201; 41 ! 23
80 46 22410101 410201; 201 ! 22101
80 47 41151 410201; 201 ! 4151
80 48 410201
Runs Count Design Lineage
80 49 51161
81 1 340 327271; 271 ! 3991; 91 ! 34
81 2 33691 327271; 271 ! 3991
81 3 33292 910; 91 ! 34
81 4 32893 910; 91 ! 34
81 5 327271
81 6 32494 910; 91 ! 34
81 7 32095 910; 91 ! 34
81 8 31696 910; 91 ! 34
81 9 31297 910; 91 ! 34
81 10 3898 910; 91 ! 34
81 11 3499 910; 91 ! 34
81 12 910
82 1 21411
84 1 283
84 2 23331
84 3 22871
84 4 22761
84 5 2233171 2226171; 61 ! 2131
84 6 2226171
84 7 221211
84 8 22031141
84 9 21461141
84 10 22421
84 11 314171 31281; 281 ! 4171
84 12 31281
84 13 41211
84 14 71121
85 1 51171
86 1 21431
87 1 31291
88 1 287 28441; 41 ! 23
88 2 28441
88 3 260111 25741111; 41 ! 23
88 4 25741111
88 5 246221 24341221; 41 ! 23
88 6 244441
88 7 24341221
88 8 81111
Runs Count Design Lineage
90 1 2133151 330301; 301 ! 21151; 151 ! 3151
90 2 21330151 330301; 301 ! 21151
90 3 215191 21451; 451 ! 5191
90 4 21451
90 5 331101 330301; 301 ! 31101
90 6 3305161 330301; 301 ! 5161
90 7 330301
90 8 32661151
90 9 51181
90 10 91101
91 1 71131
92 1 291
92 2 222231
92 3 22461
92 4 41231
93 1 31311
94 1 21471
95 1 51191
96 1 295 226423; 41 ! 23
96 2 29241 226423; 41 ! 23
96 3 28942 226423; 41 ! 23
96 4 28831 21931423; 41 ! 23
96 5 28881 24341581; 41 ! 23
96 6 28643 226423; 41 ! 23
96 7 28661 21742361; 41 ! 23
96 8 2853141 21931423; 41 ! 23
96 9 2854181 24341581; 41 ! 23
96 10 284121 218422121; 41 ! 23
96 11 28344 226423; 41 ! 23
96 12 2834161 21742361; 41 ! 23
96 13 2823142 21931423; 41 ! 23
96 14 2824281 24341581; 41 ! 23
96 15 2813181 2393141481; 41 ! 23
96 16 28141121 218422121; 41 ! 23
96 17 28045 226423; 41 ! 23
96 18 2804261 21742361; 41 ! 23
96 19 280161
96 20 2793143 21931423; 41 ! 23
96 21 2794381 24341581; 41 ! 23
96 22 2796181 2434126181; 41 ! 23
96 23 278314181 2393141481; 41 ! 23
96 24 27842121 218422121; 41 ! 23
Runs Count Design Lineage
96 25 27746 226423; 41 ! 23
96 26 2774361 21742361; 41 ! 23
96 27 27781121 24441181121; 41 ! 23
96 28 2763144 21931423; 41 ! 23
96 29 2764481 24341581; 41 ! 23
96 30 276416181 2434126181; 41 ! 23
96 31 275314281 2393141481; 41 ! 23
96 32 27543121 218422121; 41 ! 23
96 33 27447 226423; 41 ! 23
96 34 2744461 21742361; 41 ! 23
96 35 2744181121 24441181121; 41 ! 23
96 36 2733145 21931423; 41 ! 23
96 37 27331161
96 38 2734581 24341581; 41 ! 23
96 39 273426181 2434126181; 41 ! 23
96 40 272314381 2393141481; 41 ! 23
96 41 27244121 218422121; 41 ! 23
96 42 272241 212420241; 41 ! 23
96 43 27148 226423; 41 ! 23
96 44 2714561 21742361; 41 ! 23
96 45 2714281121 24441181121; 41 ! 23
96 46 27161161
96 47 2703146 21931423; 41 ! 23
96 48 2704681 24341581; 41 ! 23
96 49 270436181 2434126181; 41 ! 23
96 50 269314481 2393141481; 41 ! 23
96 51 26945121 218422121; 41 ! 23
96 52 26941241 212420241; 41 ! 23
96 53 26849 226423; 41 ! 23
96 54 2684661 21742361; 41 ! 23
96 55 2684381121 24441181121; 41 ! 23
96 56 2673147 21931423; 41 ! 23
96 57 2674781 24341581; 41 ! 23
96 58 267446181 2434126181; 41 ! 23
96 59 266314581 2393141481; 41 ! 23
96 60 26646121 218422121; 41 ! 23
96 61 26642241 212420241; 41 ! 23
96 62 265410 226423; 41 ! 23
96 63 2654761 21742361; 41 ! 23
96 64 2654481121 24441181121; 41 ! 23
96 65 2643148 21931423; 41 ! 23
96 66 2644881 24341581; 41 ! 23
96 67 264456181 2434126181; 41 ! 23
96 68 263314681 2393141481; 41 ! 23
96 69 26347121 218422121; 41 ! 23
96 70 26343241 212420241; 41 ! 23
96 71 262411 226423; 41 ! 23
96 72 2624861 21742361; 41 ! 23
Runs Count Design Lineage
96 73 2624581121 24441181121; 41 ! 23
96 74 2613149 21931423; 41 ! 23
96 75 2614981 24341581; 41 ! 23
96 76 261466181 2434126181; 41 ! 23
96 77 260314781 2393141481; 41 ! 23
96 78 26048121 218422121; 41 ! 23
96 79 26044241 212420241; 41 ! 23
96 80 259412 226423; 41 ! 23
96 81 2594961 21742361; 41 ! 23
96 82 2594681121 24441181121; 41 ! 23
96 83 25831410 21931423; 41 ! 23
96 84 25841081 24341581; 41 ! 23
96 85 258476181 2434126181; 41 ! 23
96 86 257314881 2393141481; 41 ! 23
96 87 25749121 218422121; 41 ! 23
96 88 25745241 212420241; 41 ! 23
96 89 256413 226423; 41 ! 23
96 90 25641061 21742361; 41 ! 23
96 91 2564781121 24441181121; 41 ! 23
96 92 25531411 21931423; 41 ! 23
96 93 25541181 24341581; 41 ! 23
96 94 255486181 2434126181; 41 ! 23
96 95 254314981 2393141481; 41 ! 23
96 96 254410121 218422121; 41 ! 23
96 97 25446241 212420241; 41 ! 23
96 98 253414 226423; 41 ! 23
96 99 25341161 21742361; 41 ! 23
96 100 2534881121 24441181121; 41 ! 23
96 101 25231412 21931423; 41 ! 23
96 102 25241281 24341581; 41 ! 23
96 103 252496181 2434126181; 41 ! 23
96 104 2513141081 2393141481; 41 ! 23
96 105 251411121 218422121; 41 ! 23
96 106 25147241 212420241; 41 ! 23
96 107 250415 226423; 41 ! 23
96 108 25041261 21742361; 41 ! 23
96 109 2504981121 24441181121; 41 ! 23
96 110 24931413 21931423; 41 ! 23
96 111 24941381 24341581; 41 ! 23
96 112 2494106181 2434126181; 41 ! 23
96 113 2483141181 2393141481; 41 ! 23
96 114 248412121 218422121; 41 ! 23
96 115 24848241 212420241; 41 ! 23
96 116 248481
96 117 247416 226423; 41 ! 23
96 118 24741361 21742361; 41 ! 23
96 119 24741081121 24441181121; 41 ! 23
96 120 24631414 21931423; 41 ! 23
Runs Count Design Lineage
96 121 24641481 24341581; 41 ! 23
96 122 2464116181 2434126181; 41 ! 23
96 123 2453141281 2393141481; 41 ! 23
96 124 245413121 218422121; 41 ! 23
96 125 24549241 212420241; 41 ! 23
96 126 244417 226423; 41 ! 23
96 127 24441461 21742361; 41 ! 23
96 128 24441181121
96 129 24331415 21931423; 41 ! 23
96 130 24341581
96 131 2434126181
96 132 2423141381 2393141481; 41 ! 23
96 133 242414121 218422121; 41 ! 23
96 134 242410241 212420241; 41 ! 23
96 135 241418 226423; 41 ! 23
96 136 24141561 21742361; 41 ! 23
96 137 24031416 21931423; 41 ! 23
96 138 2393141481
96 139 239415121 218422121; 41 ! 23
96 140 239411241 212420241; 41 ! 23
96 141 238419 226423; 41 ! 23
96 142 23841661 21742361; 41 ! 23
96 143 23731417 21931423; 41 ! 23
96 144 236416121 218422121; 41 ! 23
96 145 236412241 212420241; 41 ! 23
96 146 235420 226423; 41 ! 23
96 147 23541761 21742361; 41 ! 23
96 148 23431418 21931423; 41 ! 23
96 149 233417121 218422121; 41 ! 23
96 150 233413241 212420241; 41 ! 23
96 151 232421 226423; 41 ! 23
96 152 23241861 21742361; 41 ! 23
96 153 23131419 21931423; 41 ! 23
96 154 230418121 218422121; 41 ! 23
96 155 230414241 212420241; 41 ! 23
96 156 229422 226423; 41 ! 23
96 157 22941961 21742361; 41 ! 23
96 158 22831420 21931423; 41 ! 23
96 159 2273141581 212420241; 241 ! 3181; 41 ! 23
96 160 227419121 218422121; 41 ! 23
96 161 227415241 212420241; 41 ! 23
96 162 226423
96 163 22642061 21742361; 41 ! 23
96 164 22531421 21931423; 41 ! 23
96 165 2243141681 212420241; 241 ! 3181; 41 ! 23
96 166 224420121 218422121; 41 ! 23
96 167 224416241 212420241; 41 ! 23
96 168 22342161 21742361; 41 ! 23
Runs Count Design Lineage
96 169 22231422 21931423; 41 ! 23
96 170 2213141781 212420241; 241 ! 3181; 41 ! 23
96 171 221421121 218422121; 41 ! 23
96 172 221417241 212420241; 41 ! 23
96 173 22042261 21742361; 41 ! 23
96 174 21931423
96 175 2183141881 212420241; 241 ! 3181; 41 ! 23
96 176 218422121
96 177 218418241 212420241; 41 ! 23
96 178 21742361
96 179 2153141981 212420241; 241 ! 3181; 41 ! 23
96 180 215419241 212420241; 41 ! 23
96 181 2123142081 212420241; 241 ! 3181
96 182 212420241
96 183 31321
98 1 21715 714141; 141 ! 2171
98 2 21491
98 3 714141
99 1 314111 313331; 331 ! 31111
99 2 313331
99 3 91111
100 1 299
100 2 25153
100 3 24054
100 4 23453101
100 5 22955
100 6 22356 223251; 251 ! 56
100 7 223251
100 8 219520 520201; 201 ! 219
100 9 21859101
100 10 21754102 21653103; 101 ! 2151
100 11 21653103
100 12 28521 520201; 201 ! 2851
100 13 27510101
100 14 2655102 2554103; 101 ! 2151
100 15 2554103
100 16 24104
100 17 22520101 520201; 201 ! 22101
100 18 22501
100 19 2159102 58103; 101 ! 2151
100 20 41521 520201; 201 ! 4151
100 21 41251
100 22 520201
100 23 58103
Runs Count Design Lineage
102 1 2131171 21511; 511 ! 31171
102 2 21511
102 3 31341
102 4 61171
104 1 2103 210041; 41 ! 23
104 2 210041
104 3 269131 26641131; 41 ! 23
104 4 26641131
104 5 254261 25141261; 41 ! 23
104 6 252521
104 7 25141261
104 8 81131
105 1 315171 31351; 351 ! 5171
105 2 31351
105 3 51211
105 4 71151
106 1 21531
108 1 2107
108 2 24131 24061; 61 ! 2131
108 3 24061
108 4 235336 336361; 361 ! 235
108 5 23432961
108 6 227337 336361; 361 ! 22731
108 7 22733391
108 8 224271
108 9 2213162
108 10 221181
108 11 220338 336361; 361 ! 22032
108 12 22033491
108 13 21833761 336361; 361 ! 2183161
108 14 2183336191
108 15 218331181
108 16 21732962
108 17 216340 336361; 361 ! 21691; 91 ! 34
108 18 21633691 336361; 361 ! 21691
108 19 21561181
108 20 21333861 336361; 361 ! 2133261
108 21 21333662 336361; 361 ! 21362
108 22 21333061181
108 23 21363
108 24 21232963
108 25 211348 34491121; 121 ! 211; 91 ! 34
108 26 21134491 34491121; 121 ! 211
108 27 2113346191 2103336291; 61 ! 2131
Runs Count Design Lineage
108 28 211332181 21033161181; 61 ! 2131
108 29 21034461 336361; 361 ! 2103861
108 30 2103406191
108 31 21033762 336361; 361 ! 2103162
108 32 210335181 2933461181; 61 ! 2131
108 33 2103336291
108 34 21033161181
108 35 2934062 336361; 361 ! 293462
108 36 293366291
108 37 2933461181
108 38 2833663 336361; 361 ! 2863
108 39 2833062181
108 40 2732064 2331668; 61 ! 2131
108 41 2631965 2331668; 61 ! 2131
108 42 2531866 2331668; 61 ! 2131
108 43 24349 34491121; 121 ! 2431; 91 ! 34
108 44 2434591 34491121; 121 ! 2431
108 45 2433763 336361; 361 ! 243163
108 46 243336391
108 47 2433162181
108 48 2431767 2331668; 61 ! 2131
108 49 2334561 336361; 361 ! 233961
108 50 233416191
108 51 23339181
108 52 2333863 336361; 361 ! 233263
108 53 233346391
108 54 2333262181
108 55 2331668
108 56 2234861 34491121; 121 ! 2261; 91 ! 34
108 57 223446191 34491121; 121 ! 2261
108 58 22342181
108 59 2234162 336361; 361 ! 223562
108 60 223376291
108 61 2233561181
108 62 223669 34611; 61 ! 2131
108 63 22541
108 64 2134462 336361; 361 ! 3763; 61 ! 2131
108 65 213406291 3396391; 61 ! 2131
108 66 2133963 336361; 361 ! 213363
108 67 2133861181 33762181; 61 ! 2131
108 68 213356391
108 69 2133362181
108 70 2135610 34611; 61 ! 2131
108 71 34941 34491121; 121 ! 3141; 91 ! 34
108 72 348121 34491121; 91 ! 34
108 73 3454191 34491121; 121 ! 3141
108 74 34491121
108 75 34363 336361; 361 ! 3763
Runs Count Design Lineage
108 76 3396391
108 77 33762181
108 78 336361
108 79 34611
108 80 41271
110 1 2151111 21551; 551 ! 51111
110 2 21551
110 3 51221
110 4 101111
111 1 31371
112 1 2111 27543281; 281 ! 227; 41 ! 23
112 2 210841 27543281; 281 ! 227; 41 ! 23
112 3 210542 27543281; 281 ! 227; 41 ! 23
112 4 210481
112 5 210243 27543281; 281 ! 227
112 6 29671 27543281; 281 ! 21271; 41 ! 23
112 7 2934171 27543281; 281 ! 21271; 41 ! 23
112 8 2904271 27543281; 281 ! 21271; 41 ! 23
112 9 2897181
112 10 2874371 27543281; 281 ! 21271
112 11 286141 27543281; 281 ! 22141; 41 ! 23
112 12 284281 27543281; 41 ! 23
112 13 28341141 27543281; 281 ! 22141; 41 ! 23
112 14 28141281 27543281; 41 ! 23
112 15 28042141 27543281; 281 ! 22141; 41 ! 23
112 16 27981141
112 17 27842281 27543281; 41 ! 23
112 18 27743141 27543281; 281 ! 22141
112 19 2754471 27543281; 281 ! 4171
112 20 27543281
112 21 256561
112 22 24845 412281; 281 ! 227; 41 ! 23
112 23 24546 412281; 281 ! 227; 41 ! 23
112 24 24247 412281; 281 ! 227; 41 ! 23
112 25 23948 412281; 281 ! 227; 41 ! 23
112 26 23649 412281; 281 ! 227; 41 ! 23
112 27 233410 412281; 281 ! 227; 41 ! 23
112 28 2334571 412281; 281 ! 21271; 41 ! 23
112 29 230411 412281; 281 ! 227; 41 ! 23
112 30 2304671 412281; 281 ! 21271; 41 ! 23
112 31 227412 412281; 281 ! 227
112 32 2274771 412281; 281 ! 21271; 41 ! 23
112 33 22644141 412281; 281 ! 22141; 41 ! 23
112 34 2244871 412281; 281 ! 21271; 41 ! 23
112 35 22444281 412281; 41 ! 23
Runs Count Design Lineage
112 36 22345141 412281; 281 ! 22141; 41 ! 23
112 37 2214971 412281; 281 ! 21271; 41 ! 23
112 38 22145281 412281; 41 ! 23
112 39 22046141 412281; 281 ! 22141; 41 ! 23
112 40 21841071 412281; 281 ! 21271; 41 ! 23
112 41 21846281 412281; 41 ! 23
112 42 21747141 412281; 281 ! 22141; 41 ! 23
112 43 21541171 412281; 281 ! 21271; 41 ! 23
112 44 21547281 412281; 41 ! 23
112 45 21448141 412281; 281 ! 22141; 41 ! 23
112 46 21241271 412281; 281 ! 21271
112 47 21248281 412281; 41 ! 23
112 48 21149141 412281; 281 ! 22141; 41 ! 23
112 49 2949281 412281; 41 ! 23
112 50 28410141 412281; 281 ! 22141; 41 ! 23
112 51 26410281 412281; 41 ! 23
112 52 25411141 412281; 281 ! 22141; 41 ! 23
112 53 23411281 412281; 41 ! 23
112 54 22412141 412281; 281 ! 22141
112 55 41371 412281; 281 ! 4171
112 56 412281
112 57 71161
114 1 2131191 21571; 571 ! 31191
114 2 21571
114 3 31381
114 4 61191
115 1 51231
116 1 2115
116 2 224291
116 3 22581
116 4 41291
117 1 314131 313391; 391 ! 31131
117 2 313391
117 3 91131
118 1 21591
119 1 71171
120 1 2119 211641; 41 ! 23
120 2 211641
120 3 29031 2873141; 41 ! 23
120 4 2873141
120 5 28461 260601; 601 ! 22461
Runs Count Design Lineage
120 6 28351 260601; 601 ! 22351
120 7 281101 260601; 601 ! 221101
120 8 2794151
120 9 2783151 27541151; 151 ! 3151; 41 ! 23
120 10 278151 27541151; 41 ! 23
120 11 27631101 260601; 601 ! 21561101; 61 ! 2131
120 12 2765161 260601; 601 ! 21561101; 101 ! 2151
120 13 275314151 27541151; 151 ! 3151
120 14 2754161
120 15 27541101
120 16 27541151
120 17 27561101 260601; 601 ! 21561101
120 18 2703141101
120 19 270415161
120 20 2684161101
120 21 262301 25941301; 41 ! 23
120 22 26031201 260601; 601 ! 31201
120 23 26051121 260601; 601 ! 51121
120 24 260601
120 25 25941301
120 26 23061201
120 27 228101121
120 28 315181 31401; 401 ! 5181
120 29 31401
120 30 51241
120 31 81151
121 1 1112
122 1 21611
123 1 31411
124 1 2123
124 2 224311
124 3 22621
124 4 41311
125 1 531 525251; 251 ! 56
125 2 525251
126 1 2132471 324141; 141 ! 2171
126 2 21321211 32061211; 61 ! 2131
126 3 217191 21631; 631 ! 7191
126 4 21631
126 5 324141
126 6 3236171
126 7 321421
Runs Count Design Lineage
126 8 32061211
126 9 71181
126 10 91141
128 1 2127 24436161; 161 ! 45; 41 ! 23
128 2 212441 24436161; 161 ! 45; 41 ! 23
128 3 212142 24436161; 161 ! 45; 41 ! 23
128 4 212081 432321; 321 ! 4881; 41 ! 23
128 5 211843 24436161; 161 ! 45; 41 ! 23
128 6 21174181 432321; 321 ! 4881; 41 ! 23
128 7 211544 24436161; 161 ! 45; 41 ! 23
128 8 21144281 432321; 321 ! 4881; 41 ! 23
128 9 211382 2543182161; 161 ! 45; 41 ! 23
128 10 211245 24436161; 161 ! 45; 41 ! 23
128 11 2112161 24436161; 41 ! 23
128 12 21114381 432321; 321 ! 4881; 41 ! 23
128 13 21104182 2543182161; 161 ! 45; 41 ! 23
128 14 210946 24436161; 161 ! 45; 41 ! 23
128 15 210941161 24436161; 41 ! 23
128 16 21084481 432321; 321 ! 4881; 41 ! 23
128 17 21074282 2543182161; 161 ! 45; 41 ! 23
128 18 210647 24436161; 161 ! 45; 41 ! 23
128 19 210642161 24436161; 41 ! 23
128 20 210683 2442983161; 161 ! 45; 41 ! 23
128 21 21054581 432321; 321 ! 4881; 41 ! 23
128 22 210581161 2643381161; 41 ! 23
128 23 21044382 2543182161; 161 ! 45; 41 ! 23
128 24 210348 24436161; 161 ! 45; 41 ! 23
128 25 210343161 24436161; 41 ! 23
128 26 21034183 2442983161; 161 ! 45; 41 ! 23
128 27 21024681 432321; 321 ! 4881; 41 ! 23
128 28 21024181161 2643381161; 41 ! 23
128 29 21014482 2543182161; 161 ! 45; 41 ! 23
128 30 210049 24436161; 161 ! 45; 41 ! 23
128 31 210044161 24436161; 41 ! 23
128 32 21004283 2442983161; 161 ! 45; 41 ! 23
128 33 2994781 432321; 321 ! 4881; 41 ! 23
128 34 2994281161 2643381161; 41 ! 23
128 35 29984 2642684161; 161 ! 45; 41 ! 23
128 36 2984582 2543182161; 161 ! 45; 41 ! 23
128 37 29882161 2543182161; 41 ! 23
128 38 297410 24436161; 161 ! 45; 41 ! 23
128 39 29745161 24436161; 41 ! 23
128 40 2974383 2442983161; 161 ! 45; 41 ! 23
128 41 2964881 432321; 321 ! 4881; 41 ! 23
128 42 2964381161 2643381161; 41 ! 23
128 43 2964184 2642684161; 161 ! 45; 41 ! 23
128 44 296321 432321; 41 ! 23
Runs Count Design Lineage
128 45 2954682 2543182161; 161 ! 45; 41 ! 23
128 46 2954182161 2543182161; 41 ! 23
128 47 294411 24436161; 161 ! 45; 41 ! 23
128 48 29446161 24436161; 41 ! 23
128 49 2944483 2442983161; 161 ! 45; 41 ! 23
128 50 2934981 432321; 321 ! 4881; 41 ! 23
128 51 2934481161 2643381161; 41 ! 23
128 52 2934284 2642684161; 161 ! 45; 41 ! 23
128 53 29341321 432321; 41 ! 23
128 54 2924782 2543182161; 161 ! 45; 41 ! 23
128 55 2924282161 2543182161; 41 ! 23
128 56 29285 2542485161; 161 ! 45; 41 ! 23
128 57 291412 24436161; 161 ! 45; 41 ! 23
128 58 29147161 24436161; 41 ! 23
128 59 2914583 2442983161; 161 ! 45; 41 ! 23
128 60 29183161 2442983161; 41 ! 23
128 61 29041081 432321; 321 ! 4881; 41 ! 23
128 62 2904581161 2643381161; 41 ! 23
128 63 2904384 2642684161; 161 ! 45; 41 ! 23
128 64 29042321 432321; 41 ! 23
128 65 2894882 2543182161; 161 ! 45; 41 ! 23
128 66 2894382161 2543182161; 41 ! 23
128 67 2894185 2542485161; 161 ! 45; 41 ! 23
128 68 288413 24436161; 161 ! 45; 41 ! 23
128 69 28848161 24436161; 41 ! 23
128 70 2884683 2442983161; 161 ! 45; 41 ! 23
128 71 2884183161 2442983161; 41 ! 23
128 72 28741181 432321; 321 ! 4881; 41 ! 23
128 73 2874681161 2643381161; 41 ! 23
128 74 2874484 2642684161; 161 ! 45; 41 ! 23
128 75 28743321 432321; 41 ! 23
128 76 2864982 2543182161; 161 ! 45; 41 ! 23
128 77 2864482161 2543182161; 41 ! 23
128 78 2864285 2542485161; 161 ! 45; 41 ! 23
128 79 285414 24436161; 161 ! 45; 41 ! 23
128 80 28549161 24436161; 41 ! 23
128 81 2854783 2442983161; 161 ! 45; 41 ! 23
128 82 2854283161 2442983161; 41 ! 23
128 83 28586 2442286161; 161 ! 45; 41 ! 23
128 84 28441281 432321; 321 ! 4881; 41 ! 23
128 85 2844781161 2643381161; 41 ! 23
128 86 2844584 2642684161; 161 ! 45; 41 ! 23
128 87 28444321 432321; 41 ! 23
128 88 28484161 2642684161; 41 ! 23
128 89 28341082 2543182161; 161 ! 45; 41 ! 23
128 90 2834582161 2543182161; 41 ! 23
128 91 2834385 2542485161; 161 ! 45; 41 ! 23
128 92 282415 24436161; 161 ! 45; 41 ! 23
Runs Count Design Lineage
128 93 282410161 24436161; 41 ! 23
128 94 2824883 2442983161; 161 ! 45; 41 ! 23
128 95 2824383161 2442983161; 41 ! 23
128 96 2824186 2442286161; 161 ! 45; 41 ! 23
128 97 28141381 432321; 321 ! 4881; 41 ! 23
128 98 2814881161 2643381161; 41 ! 23
128 99 2814684 2642684161; 161 ! 45; 41 ! 23
128 100 28145321 432321; 41 ! 23
128 101 2814184161 2642684161; 41 ! 23
128 102 28041182 2543182161; 161 ! 45; 41 ! 23
128 103 2804682161 2543182161; 41 ! 23
128 104 2804485 2542485161; 161 ! 45; 41 ! 23
128 105 279416 24436161; 161 ! 45; 41 ! 23
128 106 279411161 24436161; 41 ! 23
128 107 2794983 2442983161; 161 ! 45; 41 ! 23
128 108 2794483161 2442983161; 41 ! 23
128 109 2794286 2442286161; 161 ! 45; 41 ! 23
128 110 27841481 432321; 321 ! 4881; 41 ! 23
128 111 2784981161 2643381161; 41 ! 23
128 112 2784784 2642684161; 161 ! 45; 41 ! 23
128 113 27846321 432321; 41 ! 23
128 114 2784284161 2642684161; 41 ! 23
128 115 27887 2342587; 41 ! 23
128 116 27741282 2543182161; 161 ! 45; 41 ! 23
128 117 2774782161 2543182161; 41 ! 23
128 118 2774585 2542485161; 161 ! 45; 41 ! 23
128 119 27785161 2542485161; 41 ! 23
128 120 276417 24436161; 161 ! 45; 41 ! 23
128 121 276412161 24436161; 41 ! 23
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Runs Count Design Lineage
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Runs Count Design Lineage
128 189 2644786 2442286161; 161 ! 45; 41 ! 23
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128 192 264641
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128 215 260412321 432321; 41 ! 23
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Runs Count Design Lineage
128 237 2574287161 2641987161; 41 ! 23
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128 256 25441084161 2642684161; 41 ! 23
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Runs Count Design Lineage
128 285 2504788 2541788161; 161 ! 45; 41 ! 23
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128 288 249426 24436161; 161 ! 45; 41 ! 23
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Runs Count Design Lineage
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128 335 243423161 24436161; 41 ! 23
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128 346 242418321 432321; 41 ! 23
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Runs Count Design Lineage
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128 382 2384688161 2541788161; 41 ! 23
128 383 23844811 25410811161; 161 ! 45; 41 ! 23
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Runs Count Design Lineage
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128 432 23242085 2542485161; 161 ! 45; 41 ! 23
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Runs Count Design Lineage
128 477 22742681161 2643381161; 41 ! 23
128 478 22742484 2642684161; 161 ! 45; 41 ! 23
128 479 227423321 432321; 41 ! 23
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128 482 22741287161 2641987161; 41 ! 23
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Runs Count Design Lineage
128 525 222430161 24436161; 41 ! 23
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128 527 22242383161 2442983161; 41 ! 23
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128 571 21842087 2342587; 41 ! 23
128 572 21841587161 2641987161; 41 ! 23
Runs Count Design Lineage
128 573 218413810 23418810; 41 ! 23
128 574 21848810161 26412810161; 41 ! 23
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128 576 21841813161 2645813161; 41 ! 23
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128 581 21741888 2541788161; 161 ! 45; 41 ! 23
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128 583 217411811 25410811161; 161 ! 45; 41 ! 23
128 584 21746811161 25410811161; 41 ! 23
128 585 21744814 2548814; 41 ! 23
128 586 216437 24436161; 161 ! 45; 41 ! 23
128 587 216432161 24436161; 41 ! 23
128 588 21643083 2442983161; 161 ! 45; 41 ! 23
128 589 21642583161 2442983161; 41 ! 23
128 590 21642386 2442286161; 161 ! 45; 41 ! 23
128 591 21641886161 2442286161; 41 ! 23
128 592 21641689 2441589161; 161 ! 45; 41 ! 23
128 593 21641189161 2441589161; 41 ! 23
128 594 21649812 2448812161; 161 ! 45; 41 ! 23
128 595 21644812161 2448812161; 41 ! 23
128 596 21642815 816161; 161 ! 45; 81 ! 2441; 41 ! 23
128 597 21543581 432321; 321 ! 4881; 41 ! 23
128 598 21543081161 2643381161; 41 ! 23
128 599 21542884 2642684161; 161 ! 45; 41 ! 23
128 600 215427321 432321; 41 ! 23
128 601 21542384161 2642684161; 41 ! 23
128 602 21542187 2342587; 41 ! 23
128 603 21541687161 2641987161; 41 ! 23
128 604 215414810 23418810; 41 ! 23
128 605 21549810161 26412810161; 41 ! 23
128 606 21547813 23411813; 41 ! 23
128 607 21542813161 2645813161; 41 ! 23
128 608 215816 816161; 161 ! 45; 41 ! 23
128 609 21443382 2543182161; 161 ! 45; 41 ! 23
128 610 21442882161 2543182161; 41 ! 23
128 611 21442685 2542485161; 161 ! 45; 41 ! 23
128 612 21442185161 2542485161; 41 ! 23
128 613 21441988 2541788161; 161 ! 45; 41 ! 23
128 614 21441488161 2541788161; 41 ! 23
128 615 214412811 25410811161; 161 ! 45; 41 ! 23
128 616 21447811161 25410811161; 41 ! 23
128 617 21445814 2548814; 41 ! 23
128 618 214814161 816161; 81 ! 2441; 41 ! 23
128 619 213438 24436161; 161 ! 45; 41 ! 23
128 620 213433161 24436161; 41 ! 23
Runs Count Design Lineage
128 621 21343183 2442983161; 161 ! 45; 41 ! 23
128 622 21342683161 2442983161; 41 ! 23
128 623 21342486 2442286161; 161 ! 45; 41 ! 23
128 624 21341986161 2442286161; 41 ! 23
128 625 21341789 2441589161; 161 ! 45; 41 ! 23
128 626 21341289161 2441589161; 41 ! 23
128 627 213410812 2448812161; 161 ! 45; 41 ! 23
128 628 21345812161 2448812161; 41 ! 23
128 629 21343815 816161; 161 ! 45; 81 ! 2441; 41 ! 23
128 630 21243681 432321; 321 ! 4881; 41 ! 23
128 631 21243181161 2643381161; 41 ! 23
128 632 21242984 2642684161; 161 ! 45; 41 ! 23
128 633 212428321 432321; 41 ! 23
128 634 21242484161 2642684161; 41 ! 23
128 635 21242287 2342587; 41 ! 23
128 636 21241787161 2641987161; 41 ! 23
128 637 212415810 23418810; 41 ! 23
128 638 212410810161 26412810161; 41 ! 23
128 639 21248813 23411813; 41 ! 23
128 640 21243813161 2645813161; 41 ! 23
128 641 21241816 816161; 161 ! 45; 41 ! 23
128 642 21143482 2543182161; 161 ! 45; 41 ! 23
128 643 21142982161 2543182161; 41 ! 23
128 644 21142785 2542485161; 161 ! 45; 41 ! 23
128 645 21142285161 2542485161; 41 ! 23
128 646 21142088 2541788161; 161 ! 45; 41 ! 23
128 647 21141588161 2541788161; 41 ! 23
128 648 211413811 25410811161; 161 ! 45; 41 ! 23
128 649 21148811161 25410811161; 41 ! 23
128 650 21146814 2548814; 41 ! 23
128 651 21141814161 816161; 81 ! 2441; 41 ! 23
128 652 210439 24436161; 161 ! 45; 41 ! 23
128 653 210434161 24436161; 41 ! 23
128 654 21043283 2442983161; 161 ! 45; 41 ! 23
128 655 21042783161 2442983161; 41 ! 23
128 656 21042586 2442286161; 161 ! 45; 41 ! 23
128 657 21042086161 2442286161; 41 ! 23
128 658 21041889 2441589161; 161 ! 45; 41 ! 23
128 659 21041389161 2441589161; 41 ! 23
128 660 210411812 2448812161; 161 ! 45; 41 ! 23
128 661 21046812161 2448812161; 41 ! 23
128 662 21044815 816161; 161 ! 45; 81 ! 2441; 41 ! 23
128 663 2943781 432321; 321 ! 4881; 41 ! 23
128 664 2943281161 2643381161; 41 ! 23
128 665 2943084 2642684161; 161 ! 45; 41 ! 23
128 666 29429321 432321; 41 ! 23
128 667 2942584161 2642684161; 41 ! 23
128 668 2942387 2342587; 41 ! 23
Runs Count Design Lineage
128 669 2941887161 2641987161; 41 ! 23
128 670 29416810 23418810; 41 ! 23
128 671 29411810161 26412810161; 41 ! 23
128 672 2949813 23411813; 41 ! 23
128 673 2944813161 2645813161; 41 ! 23
128 674 2942816 816161; 161 ! 45; 41 ! 23
128 675 2843582 2543182161; 161 ! 45; 41 ! 23
128 676 2843082161 2543182161; 41 ! 23
128 677 2842885 2542485161; 161 ! 45; 41 ! 23
128 678 2842385161 2542485161; 41 ! 23
128 679 2842188 2541788161; 161 ! 45; 41 ! 23
128 680 2841688161 2541788161; 41 ! 23
128 681 28414811 25410811161; 161 ! 45; 41 ! 23
128 682 2849811161 25410811161; 41 ! 23
128 683 2847814 2548814; 41 ! 23
128 684 2842814161 816161; 81 ! 2441
128 685 28817 816161; 161 ! 2881
128 686 27440 24436161; 161 ! 45; 41 ! 23
128 687 27435161 24436161; 41 ! 23
128 688 2743383 2442983161; 161 ! 45; 41 ! 23
128 689 2742883161 2442983161; 41 ! 23
128 690 2742686 2442286161; 161 ! 45; 41 ! 23
128 691 2742186161 2442286161; 41 ! 23
128 692 2741989 2441589161; 161 ! 45; 41 ! 23
128 693 2741489161 2441589161; 41 ! 23
128 694 27412812 2448812161; 161 ! 45; 41 ! 23
128 695 2747812161 2448812161; 41 ! 23
128 696 2745815 816161; 161 ! 45; 81 ! 2441; 41 ! 23
128 697 27815161 816161; 81 ! 2441; 41 ! 23
128 698 2643881 432321; 321 ! 4881; 41 ! 23
128 699 2643381161
128 700 2643184 2642684161; 161 ! 45
128 701 26430321 432321; 41 ! 23
128 702 2642684161
128 703 2642487 2342587; 41 ! 23
128 704 2641987161
128 705 26417810 23418810; 41 ! 23
128 706 26412810161
128 707 26410813 23411813; 41 ! 23
128 708 2645813161
128 709 2643816 816161; 161 ! 45; 41 ! 23
128 710 2543682 2543182161; 161 ! 45
128 711 2543182161
128 712 2542985 2542485161; 161 ! 45
128 713 2542485161
128 714 2542288 2541788161; 161 ! 45
128 715 2541788161
128 716 25415811 25410811161; 161 ! 45
Runs Count Design Lineage
128 717 25410811161
128 718 2548814
128 719 24441 24436161; 161 ! 45
128 720 24436161
128 721 2443483 2442983161; 161 ! 45
128 722 2442983161
128 723 2442786 2442286161; 161 ! 45
128 724 2442286161
128 725 2442089 2441589161; 161 ! 45
128 726 2441589161
128 727 24413812 2448812161; 161 ! 45
128 728 2448812161
128 729 2446815 816161; 161 ! 45; 81 ! 2441
128 730 2441815161 816161; 81 ! 2441
128 731 2343981 432321; 321 ! 4881; 41 ! 23
128 732 23431321 432321; 41 ! 23
128 733 2342587
128 734 23418810
128 735 23411813
128 736 2344816 816161; 161 ! 45; 41 ! 23
128 737 44081 432321; 321 ! 4881
128 738 432321
128 739 45816 816161; 161 ! 45
128 740 816161
129 1 31431
130 1 2151131 21651; 651 ! 51131
130 2 21651
130 3 51261
130 4 101131
132 1 2131
132 2 24331 24261; 61 ! 2131
132 3 24261
132 4 228111
132 5 22431111 224331; 331 ! 31111
132 6 224331
132 7 22261111
132 8 221221
132 9 22031221
132 10 21561221
132 11 22661
132 12 3141111 31441; 441 ! 41111
132 13 31441
132 14 41331
132 15 111121
133 1 71191
Runs Count Design Lineage
134 1 21671
135 1 33751 33291151; 151 ! 3151; 91 ! 34
135 2 336151 33291151; 91 ! 34
135 3 3335191 33291151; 151 ! 3151
135 4 33291151
135 5 327451
135 6 51271
136 1 2135 213241; 41 ! 23
136 2 213241
136 3 287171 28441171; 41 ! 23
136 4 28441171
136 5 270341 26741341; 41 ! 23
136 6 268681
136 7 26741341
136 8 81171
138 1 2131231 21691; 691 ! 31231
138 2 21691
138 3 31461
138 4 61231
140 1 2139
140 2 23871
140 3 23751 236101; 101 ! 2151
140 4 236101
140 5 234141
140 6 2275171
140 7 22551141
140 8 224351
140 9 22271101
140 10 217101141
140 11 22701
140 12 415171 41351; 351 ! 5171
140 13 41351
140 14 51281
140 15 71201
141 1 31471
142 1 21711
143 1 111131
Orthogonal Array ParentsThis next listing shows virtually all known parent orthogonal arrays up through 143 runs, areasonably comprehensive set of parent orthogonal arrays for 144 through 513 runs, and someadditional parent orthogonal arrays up through 1,000 runs. While this listing is virtually completefor the smaller arrays, new arrays are being discovered all the time. If you know of any arrays thatare not in this catalog, please email [email protected].
The number of parents up through 143 runs is fairly reasonable; currently there are 874. Beyond that,the number of parents grows at a very rapid rate. At some point, it becomes impossible to make thecatalog complete. 143 runs was chosen as the stopping point for completeness and 144 runs as thestopping point for defining child arrays. This means that this catalog has at most 144-level factors.Arrays, for example, in 288 and 432 runs are made by replacing the 144-level factor in 21441441
and 31441441 with all of the arrays in 144 runs, and replacing (72, 36, 48, 24, 18, 12, 9, 8, 6, and4)-level factors by arrays in that many runs, providing a rich mix of levels. Hence, many large andvaried arrays can be made from this catalog even if it is not complete beyond 143 runs. Beyond288 runs, 145-level and larger factors are not available, so in their place, arrays are listed that aremanufactured from the most important arrays in n > 144 runs. Such arrays are not true parents�theyjust provide a convenient mechanism to get a large catalog of arrays up through 513 runs without thecomputational burden of enabling (145 through 256)-level factors. These designs are usually of theform 23n=4.n=4/1 in n runs where the real parent would be 2n=2.n=2/1. Examples include: 2264881
in 352 runs (the real parent is 21761761) and 23001001 in 400 runs (the real parent is 22002001).Note that most arrays in this listing, even those with more than 288 runs, are true parents. Just a feware not.
This listing shows the number of parents, the total number of arrays in n runs, and a list of theparents. The 874 parents in this catalog can generate a total of 130,147 orthogonal arrays.2 All ofthe arrays in this catalog can be generated with the SAS %MktEx macro. The %MktOrth macromaintains this catalog and can be used to list and process it. For example, all of the tables in thisreport were automatically generated using the %MktOrth macro and a SAS program to write aLATEX file complete with the tabular markups. When the catalog grows, it only takes a few minutesto regenerate this entire report. The %MktRuns macro enables you to specify a design and seeall of the orthogonal arrays that fit your specification along with suggestions for sizes for smallernonorthogonal designs. See the Web book Marketing Research Methods in SAS for more information.In particular, see the chapters “Experimental Design and Choice Modeling Macros” and “DiscreteChoice” for documentation and numerous examples of their uses. The book and macros are on theWeb at http://support.sas.com/techsup/tnote/tnote_stat.html#market.
The page http://support.sas.com/techsup/technote/ts723_Designs.txt provides oneorthogonal array for every parent in this listing up through 143 runs (except for the full-factorialdesigns, which require no special expertise to generate).
2The %MktEx macro can additionally generate a number of orthogonal designs that are not explicitly in the %MktOrthcatalog, including full-factorial designs with more than 143 runs, large fractional factorial designs where the number ofruns is the power of a prime number, and larger designs with two-level factors based on large Hadamard matrices.
Parents Designs Runs
1 1 4 23
1 1 6 2131
1 2 8 2441
1 1 9 34
1 1 10 2151
4 4 12 211
2431
2261
3141
1 1 14 2171
1 1 15 3151
2 7 16 2881
45
2 3 18 2191
3661
4 4 20 219
2851
22101
4151
1 1 21 3171
1 1 22 21111
5 8 24 22041
2133141
212121
2114161
3181
1 1 25 56
1 1 26 21131
1 2 27 3991
4 4 28 227
21271
22141
4171
3 4 30 21151
31101
5161
2 20 32 216161
4881
1 1 33 31111
1 1 34 21171
1 1 35 5171
Parents Designs Runs
20 26 36 235
22731
22032
2183161
21691
2133261
21362
2103861
2103162
293462
2863
243163
233961
233263
223562
22181
213363
312121
3763
4191
1 1 38 21191
1 1 39 31131
5 8 40 23641
2254151
220201
21941101
5181
3 4 42 21211
31141
6171
4 4 44 243
216111
22221
41111
2 3 45 39151
5191
1 1 46 21231
6 58 48 24081
2333181
2316181
224241
31161
412121
1 1 49 78
2 3 50 21251
510101
1 1 51 31171
Parents Designs Runs
4 4 52 251
217131
22261
41131
3 6 54 21271
3206191
318181
1 1 55 51111
5 8 56 25241
2374171
228281
22741141
7181
1 1 57 31191
1 1 58 21291
11 15 60 259
23031
22461
22351
221101
218151
21561101
22301
31201
41151
51121
1 1 62 21311
2 3 63 312211
7191
7 123 64 232321
2541781
2541084
416161
41483
4786
89
1 1 65 51131
3 4 66 21331
31221
61111
4 4 68 267
219171
22341
41171
1 1 69 31231
3 4 70 21351
51141
71101
Parents Designs Runs
49 103 72 26841
2603141
2533241
251314161
2494191
246324161
2464162
24431241
243384161
243314162
242344162
2414163
23731341
237314163
236394161
236324163
236361
2353124161
235354162
23541181
234384162
234334163
23164
2303164
2283264
22731161121
2273664
2193204161
2183164162
2173124163
215374165
214334166
2123214161
21132061121
2113174162
2103204162
21031662121
2103134163
293164163
2931263121
283124164
28384165
273765121
27344166
26374166
263366121
25334167
324241
8191
Parents Designs Runs
1 1 74 21371
2 3 75 31251
58151
4 4 76 275
220191
22381
41191
1 1 77 71111
3 4 78 21391
31261
61131
7 49 80 27281
2615181
25581101
25143201
240401
410201
51161
2 12 81 327271
910
1 1 82 21411
12 14 84 283
23331
22871
22761
2226171
221211
22031141
21461141
22421
31281
41211
71121
1 1 85 51171
1 1 86 21431
1 1 87 31291
5 8 88 28441
25741111
244441
24341221
81111
5 10 90 21451
330301
32661151
51181
91101
1 1 91 71131
Parents Designs Runs
4 4 92 291
222231
22461
41231
1 1 93 31311
1 1 94 21471
1 1 95 51191
14 183 96 280161
27331161
27161161
248481
24441181121
24341581
2434126181
2393141481
226423
21931423
218422121
21742361
212420241
31321
2 3 98 21491
714141
2 3 99 313331
91111
15 23 100 299
25153
24054
23453101
22955
223251
21859101
21653103
27510101
2554103
24104
22501
41251
520201
58103
3 4 102 21511
31341
61171
5 8 104 210041
26641131
252521
25141261
81131
Parents Designs Runs
3 4 105 31351
51211
71151
1 1 106 21531
40 80 108 2107
24061
23432961
22733391
224271
2213162
221181
22033491
2183336191
218331181
21732962
21561181
21333061181
21363
21232963
2103406191
2103336291
21033161181
293366291
2933461181
2833062181
243336391
2433162181
233416191
23339181
233346391
2333262181
2331668
22342181
223376291
2233561181
22541
213356391
2133362181
34491121
3396391
33762181
336361
34611
41271
3 4 110 21551
51221
101111
1 1 111 31371
Parents Designs Runs
7 57 112 210481
2897181
27981141
27543281
256561
412281
71161
3 4 114 21571
31381
61191
1 1 115 51231
4 4 116 2115
224291
22581
41291
2 3 117 313391
91131
1 1 118 21591
1 1 119 71171
16 31 120 211641
2873141
2794151
2754161
27541101
27541151
2703141101
270415161
2684161101
260601
25941301
23061201
228101121
31401
51241
81151
1 1 121 1112
1 1 122 21611
1 1 123 31411
4 4 124 2123
224311
22621
41311
1 2 125 525251
7 10 126 21631
324141
3236171
321421
32061211
71181
91141
Parents Designs Runs
21 740 128 264641
2643381161
2642684161
2641987161
26412810161
2645813161
2543182161
2542485161
2541788161
25410811161
2548814
24436161
2442983161
2442286161
2441589161
2448812161
2342587
23418810
23411813
432321
816161
1 1 129 31431
3 4 130 21651
51261
101131
12 15 132 2131
24261
228111
224331
22261111
221221
22031221
21561221
22661
31441
41331
111121
1 1 133 71191
1 1 134 21671
3 6 135 33291151
327451
51271
5 8 136 213241
28441171
268681
26741341
81171
3 4 138 21691
31461
61231
Parents Designs Runs
13 15 140 2139
23871
236101
234141
2275171
22551141
224351
22271101
217101141
22701
41351
51281
71201
1 1 141 31471
1 1 142 21711
1 1 143 111131
17 1,248 144 213681
21178191
211331241
211161241
210381181
2763126481
276374165121
275334166121
274346681
272721
244311122
22334161241
2163366241
348481
436361
411122
127
1 2 147 79211
1 1 148 2147
1 5 150 511301
2 6 152 214841
276761
1 1 153 325171
1 1 156 2155
6 110 160 2144161
213847
213351161
2127101161
280801
416401
3 61 162 36561271
354541
918181
Parents Designs Runs
1 1 164 2163
2 16 168 216441
284841
1 1 169 1314
1 1 171 328191
1 1 172 2171
1 2 175 510351
4 56 176 216881
216643
288881
412441
3 24 180 2179
330601
62301
2 6 184 218041
292921
1 1 188 2187
1 4 189 336631
4 726 192 2160321
296961
448481
88241
3 12 196 2195
728281
146
1 5 198 330661
4 42 200 219641
21001001
520401
105201
1 1 204 2203
1 1 207 325231
4 72 208 220081
219843
21041041
416521
1 1 212 2211
6 259 216 221241
21081081
211377121181
372721
36665121181
67361
1 1 220 2219
5 351 224 2208161
219371161
2183141161
21121121
456561
Parents Designs Runs
3 13 225 327751
520451
156
1 1 228 2227
2 6 232 222841
21161161
1 5 234 330781
1 1 236 2235
6 302 240 223281
223043
220551241
2199101241
21201201
420601
1 2 242 1122221
2 58 243 381811
927271
1 1 244 2243
1 2 245 710351
2 6 248 224441
21241241
1 4 250 550501
3 23 252 2251
342841
62421
2 6,101 256 832321
1617
1 1 260 2259
1 2 261 327871
2 17 264 226041
21321321
1 1 268 2267
1 11 270 390901
4 136 272 226481
226243
21361361
432681
1 2 275 511551
1 1 276 2275
1 2 279 330931
2 17 280 227641
21401401
1 1 284 2283
Parents Designs Runs
8 3,207 288 2272161
225391161
2239161181
21441441
396961
436721
610481
126241
1 1 289 1718
1 1 292 2291
1 5 294 718421
1 2 296 229241
1 4 297 339991
3 24 300 2299
520601
102301
4 70 304 229681
229443
2228761
416761
1 5 306 3481021
1 1 308 2307
1 2 312 230841
1 5 315 3291051
1 1 316 2315
5 725 320 2288321
2274415
2240801
440801
810401
6 1,004 324 2323
3143121271
31081081
62541
936361
185
1 2 325 520651
1 2 328 232441
1 1 332 2331
1 2 333 3361111
6 487 336 232881
232643
229771241
2287141241
2252841
436841
1 2 338 1326261
1 1 340 2339
Parents Designs Runs
1 5 342 3301141
1 2 343 749491
1 2 344 234041
1 1 348 2347
1 5 350 520701
1 4 351 3391171
4 203 352 2336161
233047
2264881
432881
1 1 356 2355
3 133 360 235641
3481201
68601
1 1 361 1920
1 2 363 1111331
1 1 364 2363
4 150 368 236081
235843
2276921
436921
1 2 369 3301231
1 1 372 2371
1 4 375 540751
1 2 376 237241
1 11 378 3721261
1 1 380 2379
3 3,252 384 2320641
496961
816481
1 2 387 3481291
1 1 388 2387
4 28 392 238841
2196728281
728561
145281
3 24 396 2395
31321321
62661
7 996 400 239281
239043
23001001
4361001
580801
106401
206
1 1 404 2403
2 60 405 3811351
918451
Parents Designs Runs
1 2 408 240441
1 1 412 2411
1 5 414 3481381
4 299 416 2400161
239447
23121041
4481041
1 1 420 2419
1 2 423 3301411
1 2 424 242041
1 2 425 520851
1 1 428 2427
7 10,953 432 242481
238991241
2375181241
31441441
41081081
612721
126361
1 1 436 2435
1 2 440 243641
3 12 441 34277211
714631
217
1 1 444 2443
4 8,598 448 2416321
23361121
4561121
856561
3 35 450 3150511301
590901
155301
1 2 456 245241
1 2 459 37291171
1 1 460 2459
4 150 464 245681
245443
23481161
4361161
3 17 468 2467
349521
62781
1 2 472 246841
1 2 475 520951
1 1 477 337531
4 1,210 480 2464161
245847
23601201
4561201
Parents Designs Runs
3 11 484 2483
1144441
225
1 277 486 954541
1 2 488 248441
1 5 490 718701
1 1 492 2491
1 2 495 34251331
4 78 496 248881
248643
23721241
4181241
3 29 500 2499
51001001
102501
3 111 504 250041
284384841
68841
2 73,992 512 864641
1632321
1 2 513 38191191
1 1 516 2515
1 2 520 251641
1 1 524 2523
2 5 528 252081
251843
1 1 529 2324
1 2 536 253241
1 1 540 2539
2 10 544 2528161
252247
1 1 548 2547
1 2 552 254841
1 1 556 2555
2 5 560 255281
255043
1 1 564 2563
1 2 568 256441
1 1 572 2571
3 11,028 576 2544321
2530415
249
1 1 580 2579
1 2 584 258041
1 1 588 2587
2 5 592 258481
258243
1 1 596 2595
Parents Designs Runs
1 2 600 259641
1 1 604 2603
2 10 608 2592161
258647
1 1 612 2611
1 2 616 261241
1 1 620 2619
2 5 624 261681
261443
1 27 625 2526
1 1 628 2627
1 2 632 262841
1 1 636 2635
1 124 640 2576641
1 1 644 2643
1 2 648 264441
2 5 656 264881
264643
1 1 660 2659
1 2 664 266041
2 10 672 2656161
265047
2 8 676 2675
266
1 2 680 267641
1 1 684 2683
2 5 688 268081
267843
1 1 692 2691
1 2 696 269241
1 1 700 2699
2 27 704 2672321
2658415
1 1 708 2707
1 2 712 270841
2 5 720 271281
271043
1 1 724 2723
1 2 728 272441
1 435 729 2728
1 1 732 2731
2 10 736 2720161
271447
1 1 740 2739
1 2 744 274041
1 1 748 2747
2 5 752 274481
274243
Parents Designs Runs
1 1 756 2755
1 2 760 275641
1 125 768 26401281
1 2 776 277241
1 1 780 2779
3 130 784 277681
277443
285
1 1 788 2787
1 2 792 278841
1 1 796 2795
2 10 800 2784161
277847
1 1 804 2803
1 2 808 280441
1 1 812 2811
2 5 816 280881
280643
1 1 820 2819
1 2 824 282041
1 1 828 2827
2 27 832 2800321
2786415
1 2 840 283641
1 1 841 2930
1 1 844 2843
2 5 848 284081
283843
1 2 856 285241
1 1 860 2859
2 10 864 2848161
284247
1 1 868 2867
1 2 872 286841
2 5 880 287281
287043
1 1 884 2883
1 2 888 288441
1 124 896 2832641
1 1 900 2899
1 1 908 2907
2 5 912 290481
290243
1 1 916 2915
1 2 920 291641
1 1 924 2923
2 10 928 2912161
290647
Parents Designs Runs
1 2 936 293241
2 5 944 293681
293443
1 1 948 2947
2 27 960 2928321
2914415
1 1 961 3132
1 2 968 296441
1 1 972 2971
2 5 976 296881
296643
1 2 984 298041
2 10 992 2976161
297047
1 2 1000 299641
874 130,147
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