Table for CAN(6,k,7) for k up to 10000

Last Updated Mon May 9 06:41:48 MST 2016

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,7) 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 8 117649 orthogonal array 9 190715 orthogonal array fuse postop NCK 10 290569 Add 1 factors postop NCK 11 392399 Add 2 factors 12 493241 Add 3 factors 14 521017 double OA (Colbourn-Zhou) 16 537481 double OA (Colbourn-Zhou) 17 738871 Add 1 factors 18 926149 Add 2 factors 19 1088731 Add 3 factors 20 1189573 Add 4 factors 21 1257487 Add 7 factors 22 1284241 Add 7 factors 23 1290415 Add 7 factors 24 1497979 Add 7 factors 25 1697605 Add 7 factors 26 1866361 Add 7 factors 27 1962216 Martirosyan-TVT variant 28 2010166 Martirosyan-TVT 29 2028112 Martirosyan-TVT variant 30 2056882 Martirosyan-TVT 31 2084908 Martirosyan-TVT variant 32 2113678 Martirosyan-TVT 33 2439160 Martirosyan-TVT variant 34 2467678 Martirosyan-TVT 35 2677552 Martirosyan-TVT variant 36 2706322 Martirosyan-TVT 37 2941234 Add 7 factors 38 2975434 Add 7 factors 39 3104752 Add 7 factors 40 3430234 Add 7 factors 41 3460516 Add 7 factors 42 3670390 Add 7 factors 43 3699160 Add 7 factors 44 3819650 Martirosyan-TVT 45 3859142 Martirosyan-TVT variant 46 3873520 Martirosyan-TVT 48 4183714 Martirosyan-TVT 50 4416520 Martirosyan-TVT 52 4612468 Martirosyan-TVT 54 4729509 Martirosyan-TVT 56 4793089 Martirosyan-TVT 58 4811035 Martirosyan-TVT 59 4843513 Martirosyan-TVT variant 60 4886647 Martirosyan-TVT 61 5132527 Martirosyan-TVT variant 62 5350381 Martirosyan-TVT 64 5379151 Martirosyan-TVT 65 5708707 Martirosyan-TVT variant 66 5712817 Martirosyan-TVT 68 5741335 Martirosyan-TVT 70 5951209 Martirosyan-TVT 72 5979979 Martirosyan-TVT 74 6275917 Martirosyan-TVT 76 6374509 Martirosyan-TVT 78 6503827 Martirosyan-TVT 80 6894163 Martirosyan-TVT 82 6924445 Martirosyan-TVT 84 7134319 Martirosyan-TVT 86 7227943 Martirosyan-TVT 88 7348433 Martirosyan-TVT 90 7387925 Martirosyan-TVT 92 7402303 Martirosyan-TVT 96 7777453 Martirosyan-TVT 100 8010259 Martirosyan-TVT 112 8163384 Power CT16^2T8T2 128 8179848 Power CT16^2T8 144 8252914 Power CT16^2T7 160 8352768 Power CT16^2T6 176 8454598 Power CT16^2T5 192 8555440 Power CT16^2T4 196 8566752 Power CT16^2T2T2 224 8583216 Power CT16^2T2 256 8599680 Power CT16^2 257 9520530 Add 1 factors 258 9968880 Add 2 factors 259 10242594 Add 3 factors 260 10343436 Add 4 factors 263 10444278 Add 7 factors 264 11365128 Add 7 factors 272 11620530 Power CT17^2T1 289 11821920 Power CT17^2 290 12742770 Add 1 factors 291 13191120 Add 2 factors 292 13464834 Add 3 factors 293 13565676 Add 4 factors 296 13666518 Add 7 factors 297 14587368 Add 7 factors 298 15035718 Add 7 factors 299 15309432 Add 7 factors 300 15410274 Add 7 factors 303 15511116 Add 7 factors 304 16431966 Add 7 factors 305 16880316 Add 7 factors 306 16907238 Power CT19^2T2T1 307 16931934 Power CT19^2Arc(3) 320 16952448 perfect hash family32,512,16T6 352 17054278 perfect hash family32,512,16T5 384 17155120 perfect hash family32,512,16T4 448 17182896 perfect hash family32,512,16T2 512 17199360 perfect hash family32,512,16 513 18496572 Add 1 factors 514 19047822 Add 2 factors 515 19335942 Add 3 factors 516 19436784 Add 4 factors 519 19537626 Add 7 factors 529 20646624 Power CT23^2 530 21943836 Add 1 factors 531 22507728 Add 2 factors 532 22802022 Add 3 factors 533 22902864 Add 4 factors 536 23003706 Add 7 factors 537 24178096 Add 8 factors 544 24554655 Martirosyan-TVT 578 24853383 Martirosyan-TVT 580 25929141 Martirosyan-TVT 582 26377491 Martirosyan-TVT 584 26651205 Martirosyan-TVT 586 26752047 Martirosyan-TVT 592 26852889 Martirosyan-TVT 600 26962038 Power CT25^2T1 625 27161664 Power CT25^2 626 28610832 Add 1 factors 627 29235288 Add 2 factors 628 29533698 Add 3 factors 629 29634540 Add 4 factors 644 29666022 Power N-CT29^2T6T1 667 29683968 Power N-CT29^2T6 672 29873586 Power N-CT29^2T5T1 696 29891532 Power N-CT29^2T5 700 30073212 Power N-CT29^2T4T1 725 30091158 Power N-CT29^2T4 728 30241968 Power N-CT29^2T3T1 754 30259914 Power N-CT29^2T3 756 30337823 Power N-CT29^2T2T1 783 30355769 Power N-CT29^2T2 784 30385773 Power N-CT29^2T1T1 812 30403719 Power N-CT29^2T1 841 30421665 Power N-CT29^2 842 30853215 Power N-CT29^2+1 843 31161501 Power N-CT31^2Arc(4) 870 31188783 Power N-CT31^2T2T1 871 31189527 Power N-CT31^2Arc(3) 899 31216809 Power N-CT31^2T2 900 31217553 Power N-CT31^2T1T1 930 31245579 Power N-CT31^2T1 961 31273605 Power N-CT31^2 962 31705155 Power N-CT31^2+1 963 33323079 Add 1 factors 992 33790062 Power CT32^2T1 1024 33818832 Power CT32^2 1025 35454354 Add 1 factors 1026 36116148 Add 2 factors 1027 36457776 Add 3 factors 1028 36558618 Add 4 factors 1031 36659460 Add 7 factors 1032 37785829 Martirosyan-Colbourn 1036 37973107 Martirosyan-Colbourn 1038 38044759 Martirosyan-Colbourn 1058 39153757 Martirosyan-Colbourn 1060 40450969 Martirosyan-Colbourn 1062 41014861 Martirosyan-Colbourn 1064 41309155 Martirosyan-Colbourn 1066 41409997 Martirosyan-Colbourn 1072 41510839 Martirosyan-Colbourn 1101 42239199 Power N-CT37^2Arc(8) 1131 42474111 Power N-CT37^2Arc(7) 1162 42709023 Power N-CT37^2Arc(6) 1194 42943935 Power N-CT37^2Arc(5) 1227 43178847 Power N-CT37^2Arc(4) 1261 43413759 Power N-CT37^2Arc(3) 1296 43648671 Power N-CT37^2T1T1 1332 43883583 Power N-CT37^2T1 1369 44118495 Power N-CT37^2 1370 44631495 Power N-CT37^2+1 1371 46318173 Add 1 factors 1372 46853871 Add 3 factors 1373 46954713 Add 4 factors 1376 47055555 Add 7 factors 1410 47250600 Power N-CT41^2Trin2,2,3 1447 47379918 Power N-CT41^2Trin2,2,2 1482 47606364 Power N-CT41^2T3T2 1484 47705400 Power N-CT41^2Trin1,2,2 1521 47735682 Power N-CT41^2T2T2 1558 47962128 Power N-CT41^2T3 1560 48061164 Power N-CT41^2T2T1 1599 48091446 Power N-CT41^2T2 1600 48386646 Power N-CT41^2T1T1 1640 48416928 Power N-CT41^2T1 1681 48447210 Power N-CT41^2 1682 50251866 Add 1 factors 1684 50794516 Martirosyan-Colbourn 1686 51102802 Martirosyan-Colbourn 1688 51130084 Martirosyan-Colbourn 1696 51153694 Martirosyan-Colbourn 1728 51155386 Martirosyan-Colbourn 1740 51225118 Martirosyan-Colbourn 1742 51225862 Martirosyan-Colbourn 1792 51253144 Martirosyan-Colbourn 1798 51297556 Martirosyan-Colbourn 1800 51298300 Martirosyan-Colbourn 1824 51354352 Martirosyan-Colbourn 1860 51374116 Martirosyan-Colbourn 1920 51402142 Martirosyan-Colbourn 1922 51446560 Martirosyan-Colbourn 1924 51878110 Martirosyan-Colbourn 1926 53496034 Martirosyan-Colbourn 1944 53963017 Martirosyan-Colbourn 1960 54009457 Martirosyan-Colbourn 1984 54032569 Martirosyan-Colbourn 2016 54061339 Martirosyan-Colbourn 2048 54072643 Martirosyan-Colbourn 2049 55896409 Add 1 factors 2050 56092465 Martirosyan-Colbourn 2052 56754259 Martirosyan-Colbourn 2054 57095887 Martirosyan-Colbourn 2055 57156787 Add 7 factors 2056 57196729 Martirosyan-Colbourn 2062 57532183 Martirosyan-Colbourn 2071 57641400 Power N-CT47^2Arc(3) 2116 57951594 Power N-CT47^2T1T1 2162 58261788 Power N-CT47^2T1 2210 58571982 Power N-CT47^2+1 2304 59643070 Power CT31^3T22T15T15 2560 59742924 Power CT31^3T21T15T15 2816 59844754 Power CT31^3T20T15T15 3072 59945596 Power CT31^3T19T15T15 3136 59956908 Power CT31^3T17T17T15 3584 59973372 Power CT31^3T17T15T15 4096 59989836 Power CT31^3T15T15T15 4352 60191226 Power CT31^3T15T15T14 4608 60378504 Power CT31^3T15T15T13 4624 60392616 Power CT31^3T15T14T14 4864 60541086 Power CT31^3T15T15T12 4896 60579894 Power CT31^3T15T14T13 4913 60594006 Power CT31^3T14T14T14 5120 60641928 Power CT31^3T15T15T11 5376 60709842 Power CT31^3T15T15T10 5632 60736596 Power CT31^3T15T15T9 5888 60742770 Power CT31^3T15T15T8 5984 60937986 Power CT31^3T15T14T9 6256 60944160 Power CT31^3T15T14T8 6336 61125264 Power CT31^3T15T13T9 6624 61131438 Power CT31^3T15T13T8 6647 61145550 Power CT31^3T14T14T8 6688 61287846 Power CT31^3T15T12T9 6992 61294020 Power CT31^3T15T12T8 7038 61332828 Power CT31^3T14T13T8 7040 61388688 Power CT31^3T15T11T9 7360 61394862 Power CT31^3T15T11T8 7392 61456602 Power CT31^3T15T10T9 7728 61462776 Power CT31^3T15T10T8 7744 61483356 Power CT31^3T15T9T9 8096 61489530 Power CT31^3T15T9T8 8464 61495704 Power CT31^3T15T8T8 8602 61690920 Power CT31^3T14T9T8 8993 61697094 Power CT31^3T14T8T8 9108 61878198 Power CT31^3T13T9T8 9522 61884372 Power CT31^3T13T8T8 9614 62040780 Power CT31^3T12T9T8 10000 62046954 Power CT31^3T12T8T8

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