Table for CAN(6,k,3) for k up to 10000

Last Updated Sun Nov 22 06:45:17 MST 2009

Locate the k in the first column that is at least as large as the number of factors in which you are interested. Then let N be the number of rows (tests) given in the second column. A CA(N;6,k,3) exists according to a construction in the reference (cryptically) given in the third column. The accompanying graph plots N vertically against log k (base 10).

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k N Source 7 729 orthogonal array 8 1152 cross-sum (CKRS) 11 1449 Walker-Colbourn 12 2403 Add a factor 13 2806 Density (Colbourn) postop NCK 14 3091 Density (Colbourn) postop NCK 15 3384 Density (Colbourn) postop NCK 16 3577 Density (Linnemann-Frewer) postop NCK 17 3866 Density (Colbourn) postop NCK 18 4085 Density (Linnemann-Frewer) postop NCK 19 4299 Density (Linnemann-Frewer) postop NCK 20 4501 Density (Colbourn) postop NCK 21 4686 Density (Colbourn) postop NCK 22 4864 Density (Colbourn) postop NCK 24 5193 Density (Colbourn) postop NCK 25 5564 IPOG-F (NIST) 26 5709 IPOG-F (NIST) 27 5853 IPOG-F (NIST) 28 6003 IPOG-F (NIST) 29 6150 IPOG-F (NIST) 30 6281 IPOG-F (NIST) 31 6413 IPOG-F (NIST) 32 6535 IPOG-F (NIST) 33 6656 IPOG-F (NIST) 34 6772 IPOG-F (NIST) 35 6877 IPOG-F (NIST) 36 6989 IPOG-F (NIST) 37 7092 IPOG-F (NIST) 38 7194 IPOG-F (NIST) 39 7293 IPOG-F (NIST) 40 7391 IPOG-F (NIST) 41 7490 IPOG-F (NIST) 42 7574 IPOG-F (NIST) 43 7672 IPOG-F (NIST) 44 7757 IPOG-F (NIST) 45 7845 IPOG-F (NIST) 46 7938 IPOG-F (NIST) 47 8013 IPOG-F (NIST) 48 8092 IPOG-F (NIST) 49 8179 IPOG-F (NIST) 50 8256 IPOG-F (NIST) 51 8333 IPOG-F (NIST) 52 11627 Add a factor 53 14921 Add a factor 54 18281 Add a factor 55 21671 Add a factor 56 25079 Add a factor 57 28511 Add a factor 58 29045 Martirosyan-Colbourn 60 29240 Martirosyan-Colbourn 62 29440 Martirosyan-Colbourn 72 29553 perfect hash familyMOLR(13:12,6) 74 30575 Martirosyan-Colbourn 76 30733 Martirosyan-Colbourn 78 30878 Martirosyan-Colbourn 81 31884 Power 13^2T2S8 87 32287 Power 13^2T2S7 92 32690 Power 13^2T2S6 98 33093 Power 13^2T2S5 105 33496 Power 13^2T2S4 121 33751 Power 13^2T2T2 122 34302 Power 13^2T2S2 132 34705 Power 13^2T2T1 143 35108 Power 13^2T2 144 35659 Power 13^2T1T1 156 36062 Power 13^2T1 169 36465 Power 13^2 170 40170 Power 13^2+1 171 43979 Power 13^2+2 176 44360 Power 16^2T5 180 45121 Power 16^2T4T1 182 45231 Power 16^2T3T2 192 45314 Power 16^2T4 196 45516 Power 16^2T2T2 197 45616 Power 16^2T2S2 198 45716 Power 16^2S4 208 45717 Power 16^2T3 210 45809 Power 16^2T2T1 211 45909 Power 16^2S3 224 46002 Power 16^2T2 225 46102 Power 16^2T1T1 240 46295 Power 16^2T1 256 46488 Power 16^2 272 49956 Power 17^2T1 289 50245 Power 17^2 290 53092 Power 17^2+1 291 55018 Power 19^2S4 304 55152 Power 19^2T3 306 55227 Power 19^2T2T1 307 55232 Power 19^2S3 323 55441 Power 19^2T2 324 55446 Power 19^2T1T1 342 55660 Power 19^2T1 361 55874 Power 19^2 362 58500 Power 19^2+1 363 60905 Power 19^2+2 364 63219 Power 19^2+3 373 64864 Power 23^2S8 389 65193 Power 23^2S7 406 65522 Power 23^2S6 424 65851 Power 23^2S5 443 66180 Power 23^2S4 463 66509 Power 23^2S3 484 66838 Power 23^2T1T1 506 67167 Power 23^2T1 530 67496 Power 23^2+1 531 70835 Power 25^2S4 553 71206 Power 25^2S3 576 71577 Power 25^2T1T1 600 71948 Power 25^2T1 625 72319 Power 25^2 626 74204 Power 25^2+1 648 75416 Power 27^2T3 650 75643 Power 27^2T2T1 651 75644 Power 27^2S3 675 75787 Power 27^2T2 676 75788 Power 27^2T1T1 702 75932 Power 27^2T1 729 76076 Power 27^2 730 78026 Power 27^2+1 731 79349 Power 29^2S4 756 79493 Power 29^2T2T1 757 79496 Power 29^2S3 783 79640 Power 29^2T2 784 79643 Power 29^2T1T1 812 79790 Power 29^2T1 841 79937 Power 29^2 842 81640 Power 29^2+1 843 82828 Power 31^2S4 868 82946 Power 31^2T3 871 82960 Power 31^2S3 900 83092 Power 31^2T1T1 930 83224 Power 31^2T1 961 83356 Power 31^2 992 84820 Power 32^2T1 1024 84942 Power 32^2 1025 86515 Power 32^2+1 1026 88023 Power 32^2+2 1027 89388 Power 32^2+3 1028 90844 Power 32^2 +4 1029 91092 Power 37^2T6S4 1036 91094 Power 37^2T9 1038 91129 Power 37^2T4S6 1044 91138 Power 37^2T8T1 1050 91157 Power 37^2T7T2 1051 91166 Power 37^2T7S2 1054 91184 Power 37^2T6T3 1056 91190 Power 37^2T5T4 1057 91195 Power 37^2T6S3 1062 91214 Power 37^2T5S4 1066 91232 Power 37^2T4S5 1073 91241 Power 37^2T8 1080 91269 Power 37^2T7T1 1085 91289 Power 37^2T6T2 1086 91298 Power 37^2T6S2 1088 91306 Power 37^2T5T3 1089 91311 Power 37^2T4T4 1091 91317 Power 37^2T5S3 1095 91335 Power 37^2T4S4 1098 91348 Power 37^2T3S5 1100 91350 Power 37^2T2S6 1101 91359 Power 37^2S8 1110 91372 Power 37^2T7 1116 91401 Power 37^2T6T1 1120 91411 Power 37^2T5T2 1121 91420 Power 37^2T5S2 1122 91427 Power 37^2T4T3 1125 91438 Power 37^2T4S3 1128 91451 Power 37^2T3S4 1130 91453 Power 37^2T2S5 1131 91462 Power 37^2S7 1147 91504 Power 37^2T6 1152 91523 Power 37^2T5T1 1155 91532 Power 37^2T4T2 1156 91541 Power 37^2T4S2 1159 91554 Power 37^2T3S3 1161 91556 Power 37^2T2S4 1162 91565 Power 37^2S6 1184 91626 Power 37^2T5 1188 91644 Power 37^2T4T1 1190 91648 Power 37^2T3T2 1191 91657 Power 37^2T3S2 1193 91659 Power 37^2T2S3 1194 91668 Power 37^2S5 1221 91747 Power 37^2T4 1225 91753 Power 37^2T2T2 1226 91762 Power 37^2T2S2 1227 91771 Power 37^2S4 1258 91863 Power 37^2T3 1260 91865 Power 37^2T2T1 1261 91874 Power 37^2S3 1295 91968 Power 37^2T2 1296 91977 Power 37^2T1T1 1332 92080 Power 37^2T1 1369 92183 Power 37^2 1370 93509 Power 37^2+1 1371 94796 Power 37^2+2 1372 96070 Power 37^2+3 1375 96563 Power 41^2T4S4 1381 96565 Power 41^2S8 1394 96639 Power 41^2T7 1400 96645 Power 41^2T6T1 1405 96658 Power 41^2T5S2 1409 96662 Power 41^2T4S3 1415 96664 Power 41^2S7 1435 96744 Power 41^2T6 1440 96757 Power 41^2T5T1 1444 96761 Power 41^2T4S2 1450 96763 Power 41^2S6 1476 96856 Power 41^2T5 1480 96860 Power 41^2T4T1 1486 96862 Power 41^2S5 1517 96959 Power 41^2T4 1523 96961 Power 41^2S4 1561 97060 Power 41^2S3 1600 97159 Power 41^2T1T1 1640 97258 Power 41^2T1 1681 97357 Power 41^2 1682 98449 Power 41^2+1 1683 99331 Power 43^2S4 1723 99429 Power 43^2S3 1764 99527 Power 43^2T1T1 1806 99625 Power 43^2T1 1849 99723 Power 43^2 1850 100828 Power 43^2+1 1851 101972 Power 43^2+2 1852 103181 Power 43^2+3 1855 103515 Power 47^2T4S4 1858 103525 Power 47^2T3S5 1880 103534 Power 47^2T7 1890 103549 Power 47^2T5T2 1892 103559 Power 47^2T4T3 1895 103590 Power 47^2T4S3 1898 103600 Power 47^2T3S4 1900 103613 Power 47^2T2S5 1901 103631 Power 47^2S7 1927 103633 Power 47^2T6 1932 103642 Power 47^2T5T1 1936 103644 Power 47^2T3T3 1939 103675 Power 47^2T3S3 1941 103688 Power 47^2T2S4 1942 103706 Power 47^2S6 1974 103717 Power 47^2T5 1980 103732 Power 47^2T3T2 1981 103750 Power 47^2T3S2 1983 103763 Power 47^2T2S3 1984 103781 Power 47^2S5 2021 103815 Power 47^2T4 2025 103820 Power 47^2T2T2 2026 103838 Power 47^2T2S2 2027 103856 Power 47^2S4 2068 103900 Power 47^2T3 2070 103913 Power 47^2T2T1 2071 103931 Power 47^2S3 2115 103988 Power 47^2T2 2116 104006 Power 47^2T1T1 2162 104081 Power 47^2T1 2209 104156 Power 47^2 2210 105183 Power 47^2+1 2211 105966 Power 49^2S4 2257 106053 Power 49^2S3 2304 106140 Power 49^2T1T1 2352 106227 Power 49^2T1 2401 106314 Power 49^2 2402 107315 Power 49^2+1 2403 108316 Power 49^2+2 2404 120148 Add a factor 2408 125759 Power 25^3T17S24 3311 126056 Power 25^3T14S24 3333 126427 Power 25^3T14S23 3366 126798 Power 25^3T14S22 3612 127010 Power 25^3T13S24 3636 127381 Power 25^3T13S23 3913 127413 Power 25^3T12S24 4214 127698 Power 25^3T11S24 4515 127991 Power 25^3T10S24 4816 128184 Power 25^3T9S24 5117 128473 Power 25^3T8S24 5418 128692 Power 25^3T7S24 5719 128906 Power 25^3T6S24 6020 129108 Power 25^3T5S24 6321 129293 Power 25^3T4S24 6622 129471 Power 25^3T3S24 7224 129800 Power 25^3S25 7272 130171 Power 25^3S24 7344 130542 Power 25^3S23 7440 130913 Power 25^3S22 7560 131284 Power 25^3S21 7704 131655 Power 25^3S20 7872 132026 Power 25^3S19 8064 132397 Power 25^3S18 8280 132768 Power 25^3S17 8520 133139 Power 25^3S16 8784 133510 Power 25^3S15 9072 133881 Power 25^3S14 9384 134252 Power 25^3S13 9720 134623 Power 25^3S12 10000 134994 Power 25^3S11

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