Table for CAN(6,k,9) 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,9) 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 10 531441 orthogonal array 11 997272 extended OA (Colbourn) 12 1469664 Add 1 factors 13 1942056 Add 2 factors 14 2414448 Add 3 factors 18 2421009 double OA (Colbourn-Zhou) 20 2479329 double OA (Colbourn-Zhou) 21 3423465 Add 1 factors 22 4315761 Add 2 factors 23 5068089 Add 3 factors 24 5540481 Add 4 factors 26 5890401 Add 9 factors 27 5931225 Add 9 factors 29 6012873 Add 9 factors 30 6974505 Add 9 factors 31 7954281 Add 9 factors 32 9144526 Martirosyan-TVT 33 9144582 Martirosyan-TVT variant 34 9328164 Martirosyan-TVT 35 9329964 Martirosyan-TVT variant 36 9434868 Martirosyan-TVT 38 9493756 Martirosyan-TVT 39 9583324 Martirosyan-TVT variant 40 9662002 Martirosyan-TVT 41 11077882 Add 1 factors 42 11782472 Martirosyan-TVT 43 12909130 Add 3 factors 44 13381522 Add 4 factors 45 13626780 Add 9 factors 47 13685668 Add 9 factors 48 13775236 Add 9 factors 49 13853914 Add 9 factors 50 15270946 Add 9 factors 51 15975536 Add 9 factors 52 17107378 Add 9 factors 53 17749212 Martirosyan-TVT variant 54 17788542 Martirosyan-TVT 56 17891494 Martirosyan-TVT 57 17981062 Martirosyan-TVT variant 58 18020392 Martirosyan-TVT 59 19107072 Martirosyan-TVT variant 60 19146402 Martirosyan-TVT 61 20126178 Martirosyan-TVT variant 62 20283498 Martirosyan-TVT 63 21473743 Martirosyan-TVT variant 64 21513073 Martirosyan-TVT 66 21513129 Martirosyan-TVT 68 21696711 Martirosyan-TVT 70 21698511 Martirosyan-TVT 72 21803415 Martirosyan-TVT 76 22224071 Martirosyan-TVT 78 22313639 Martirosyan-TVT 79 22394765 Martirosyan-TVT variant 80 22397213 Martirosyan-TVT 82 23813669 Martirosyan-TVT 83 24529851 Martirosyan-TVT variant 84 24541507 Martirosyan-TVT 85 26671845 Martirosyan-TVT variant 87 27293519 Add 9 factors 88 27374645 Add 9 factors 89 27377093 Add 9 factors 90 28393175 Martirosyan-TVT 94 28517151 Martirosyan-TVT 96 28606719 Martirosyan-TVT 98 28685973 Martirosyan-TVT 100 30103005 Martirosyan-TVT 101 31464883 Martirosyan-TVT variant 102 32122171 Martirosyan-TVT 104 33254013 Martirosyan-TVT 106 33895847 Martirosyan-TVT 108 33935177 Martirosyan-TVT 112 34064049 Martirosyan-TVT 114 34154193 Martirosyan-TVT 116 34193523 Martirosyan-TVT 118 35280203 Martirosyan-TVT 120 35319533 Martirosyan-TVT 121 35888654 Power CT16^2T5T5 122 36299309 Martirosyan-TVT 132 36361046 Power CT16^2T5T4 144 36833438 Power CT16^2T4T4 170 36846560 Power CT17^2T7 187 37312391 Power CT17^2T6 190 37721360 Power CT19^2T9 204 37784783 Power CT17^2T5 209 38187191 Power CT19^2T8 221 38257175 Power CT17^2T4 228 38659583 Power CT19^2T7 238 38729567 Power CT17^2T3 290 38736128 Power CT17^2+1 291 39435968 Power CT19^2Arc(4) 307 39494288 Power CT19^2Arc(3) 324 39552608 Power CT19^2T1T1 342 39610928 Power CT19^2T1 362 39669248 Power CT19^2+1 363 43600520 Add 1 factors 364 45752528 Add 2 factors 365 47064728 Add 3 factors 366 47537120 Add 4 factors 371 48009512 Add 9 factors 372 51940784 Add 9 factors 373 54092792 Add 9 factors 374 55404992 Add 9 factors 375 55877384 Add 9 factors 379 56349776 Add 9 factors 380 56358920 Add 9 factors 381 60290840 Add 9 factors 382 62442848 Add 9 factors 383 63755048 Add 9 factors 384 64227440 Add 9 factors 388 64699832 Add 9 factors 389 65181296 Add 9 factors 390 69113216 Add 9 factors 391 71265224 Add 9 factors 392 72577424 Add 9 factors 393 73049816 Add 9 factors 397 73522208 Add 9 factors 398 74003672 Add 9 factors 400 75911888 Power CT23^2T3T3 402 76103696 Power CT23^2Arc(6):1 twos,1 ones 3 ext 403 76155536 Power CT23^2Arc(6):3 twos,0 ones 404 76295504 Power CT23^2Arc(8):2 twos,2 ones 405 76435472 Power CT23^2Arc(4)T2 406 76575440 Power CT23^2Arc(6) 420 76856024 Power CT23^2T3T2 421 76995992 Power CT23^2Arc(2)T3 422 77047832 Power CT23^2Arc(6):2 twos,1 ones 423 77187800 Power CT23^2Arc(3)T2 424 77327768 Power CT23^2Arc(5) 448 77465695 perfect hash family32,512,16T2 514 77472256 perfect hash family32,514,18 516 79338496 perfect hash family32,516,20 529 81089408 Power CT23^2 530 85806920 Add 1 factors 540 86577888 Power N-CT29^2T9T2 580 86659536 Power N-CT29^2T9 609 87603672 Power N-CT29^2T8 638 88495968 Power N-CT29^2T7 667 89248296 Power N-CT29^2T6 696 89720688 Power N-CT29^2T5 702 89988960 Power N-CT29^2T3T2 729 90029784 Power N-CT29^2T2T2 754 90070608 Power N-CT29^2T3 783 90111432 Power N-CT29^2T2 841 90193080 Power N-CT29^2 842 95852640 Add 1 factors 843 98304672 Add 2 factors 844 99616872 Add 3 factors 845 100089264 Add 4 factors 850 100561656 Add 9 factors 851 106221432 Add 9 factors 852 108673464 Add 9 factors 853 109985664 Add 9 factors 854 110458056 Add 9 factors 859 110930448 Add 9 factors 871 116374872 Power N-CT31^2Arc(3) 900 117354648 Power N-CT31^2T1T1 930 118334424 Power N-CT31^2T1 961 119314200 Power N-CT31^2 962 125738904 Add 1 factors 963 128445600 Add 2 factors 964 129757800 Add 3 factors 965 130230192 Add 4 factors 970 130702584 Add 9 factors 987 134750594 Power N-CT41^2T8S13 1016 134934176 Power N-CT41^2T7S13 1046 134935976 Power N-CT41^2T6S13 1076 135040880 Power N-CT41^2T5S13 1134 135099768 Power N-CT41^2T3S13 1164 135189336 Power N-CT41^2T2S13 1198 135268014 Power N-CT41^2Arc(14) 1226 136683894 Power N-CT41^2Arc(13) 1255 138099774 Power N-CT41^2Arc(12) 1285 139515654 Power N-CT41^2Arc(11) 1316 140931534 Power N-CT41^2Arc(10) 1348 142347414 Power N-CT41^2Arc(9) 1370 142406325 Power N-CT37^2+1 1371 143749845 Power N-CT37^2+2 1381 143763294 Power N-CT41^2Arc(8) 1415 145179174 Power N-CT41^2Arc(7) 1450 146595054 Power N-CT41^2Arc(6) 1486 148010934 Power N-CT41^2Arc(5) 1523 149426814 Power N-CT41^2Arc(4) 1561 150842694 Power N-CT41^2Arc(3) 1600 152258574 Power N-CT41^2T1T1 1640 153674454 Power N-CT41^2T1 1681 155090334 Power N-CT41^2 1682 162732198 Add 1 factors 1683 166003302 Add 2 factors 1684 167595438 Add 3 factors 1685 168067830 Add 4 factors 1690 168540222 Add 9 factors 1691 176182086 Add 9 factors 1723 177347832 Power N-CT43^2Arc(3) 1764 178474490 Power N-CT43^2T1T1 1806 179601148 Power N-CT43^2T1 1849 180727806 Power N-CT43^2 1850 187341294 Power N-CT43^2+1 1880 187575672 Power N-CT47^2T7 1927 188991552 Power N-CT47^2T6 1974 189696142 Power N-CT47^2T5 2021 190822800 Power N-CT47^2T4 2068 191295192 Power N-CT47^2T3 2115 191540450 Power N-CT47^2T2 2209 191599338 Power N-CT47^2 2210 192853290 Power N-CT47^2+1 2211 193954782 Power N-CT47^2+2 2212 202284966 Add 1 factors 2213 205423914 Add 4 factors 2218 205896306 Add 9 factors 2219 207150258 Add 9 factors 2220 208251750 Add 9 factors 3602 209766560 Power CT31^3T21S30 3962 210232391 Power CT31^3T20S30 4320 210704783 Power CT31^3T19S30 4680 211177175 Power CT31^3T18S30 5040 211649567 Power CT31^3T17S30 6477 211656128 Power CT31^3T13S30 7197 211714448 Power CT31^3T11S30 7555 212658584 Power CT31^3T10S30 7915 213550880 Power CT31^3T9S30 8275 214303208 Power CT31^3T8S30 8633 214775600 Power CT31^3T7S30 9351 215125520 Power CT31^3T5S30 9711 215166344 Power CT31^3T4S30 10000 215247992 Power CT31^3T2S30

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