Table for CAN(6,k,9) for k up to 10000

Last Updated Fri Sep 20 11:45:18 MST 2013

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 9190017 Add 9 factors 34 9432468 Martirosyan-Tran van Trung 36 9537372 Martirosyan-Tran van Trung 38 9595692 Martirosyan-Tran van Trung 40 9674370 Martirosyan-Tran van Trung 41 11090250 Add 1 factors 42 11798712 Martirosyan-Tran van Trung 43 12921498 Add 3 factors 44 13393890 Add 4 factors 45 13729284 Add 9 factors 47 13787604 Add 9 factors 49 13866282 Add 9 factors 50 16064946 Add 9 factors 51 16773408 Add 9 factors 52 17774604 Martirosyan-Tran van Trung 54 17891046 Martirosyan-Tran van Trung 56 17993430 Martirosyan-Tran van Trung 58 18032760 Martirosyan-Tran van Trung 60 19618786 Martirosyan-Tran van Trung 62 20755882 Martirosyan-Tran van Trung 64 22503332 Martirosyan-Tran van Trung 68 22745783 Martirosyan-Tran van Trung 72 22850687 Martirosyan-Tran van Trung 76 22909007 Martirosyan-Tran van Trung 78 22987685 Martirosyan-Tran van Trung 79 25186349 Add 1 factors 80 26130485 Add 2 factors 81 27022781 Add 3 factors 82 27495173 Add 4 factors 85 27888887 Add 9 factors 87 27967565 Add 9 factors 88 30057285 Martirosyan-Tran van Trung 90 30392679 Martirosyan-Tran van Trung 94 30450999 Martirosyan-Tran van Trung 98 30529677 Martirosyan-Tran van Trung 100 32728341 Martirosyan-Tran van Trung 102 33667293 Martirosyan-Tran van Trung 104 34437999 Martirosyan-Tran van Trung 108 34554441 Martirosyan-Tran van Trung 110 34656825 Martirosyan-Tran van Trung 112 35070897 Martirosyan-Tran van Trung 116 35524299 Martirosyan-Tran van Trung 121 35888654 Power CT16^2T5T5 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 44113808 Add 1 factors 364 46265816 Add 2 factors 365 47578016 Add 3 factors 366 48050408 Add 4 factors 371 48522800 Add 9 factors 372 52967360 Add 9 factors 373 55119368 Add 9 factors 374 56431568 Add 9 factors 375 56903960 Add 9 factors 379 57376352 Add 9 factors 380 57381536 Add 9 factors 381 61826096 Add 9 factors 382 63978104 Add 9 factors 383 65290304 Add 9 factors 384 65762696 Add 9 factors 388 66235088 Add 9 factors 389 66240272 Add 9 factors 390 70684832 Add 9 factors 391 72836840 Add 9 factors 392 74149040 Add 9 factors 393 74621432 Add 9 factors 397 75093824 Add 9 factors 398 75099008 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 98305968 Add 2 factors 844 99618168 Add 3 factors 845 100090560 Add 4 factors 850 100562952 Add 9 factors 851 106222728 Add 9 factors 852 108676056 Add 9 factors 853 109988256 Add 9 factors 854 110460648 Add 9 factors 859 110933040 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 1016 135199264 Power N-CT41^2T7S13 1076 135304168 Power N-CT41^2T5S13 1134 135362488 Power N-CT41^2T3S13 1198 135441166 Power N-CT41^2Arc(14) 1226 136857046 Power N-CT41^2Arc(13) 1255 138272926 Power N-CT41^2Arc(12) 1285 139688806 Power N-CT41^2Arc(11) 1316 141104686 Power N-CT41^2Arc(10) 1348 142520566 Power N-CT41^2Arc(9) 1370 143935365 Power N-CT37^2+1 1381 143936446 Power N-CT41^2Arc(8) 1415 145352326 Power N-CT41^2Arc(7) 1450 146768206 Power N-CT41^2Arc(6) 1486 148184086 Power N-CT41^2Arc(5) 1523 149599966 Power N-CT41^2Arc(4) 1561 151015846 Power N-CT41^2Arc(3) 1600 152431726 Power N-CT41^2T1T1 1640 153847606 Power N-CT41^2T1 1681 155263486 Power N-CT41^2 1682 162905350 Add 1 factors 1683 166177750 Add 2 factors 1684 167769886 Add 3 factors 1685 168242278 Add 4 factors 1690 168714670 Add 9 factors 1691 176356534 Add 9 factors 1723 177532600 Power N-CT43^2Arc(3) 1764 178655386 Power N-CT43^2T1T1 1806 179778172 Power N-CT43^2T1 1849 180900958 Power N-CT43^2 1850 187514446 Power N-CT43^2+1 1880 188913208 Power N-CT47^2T7 1927 190329088 Power N-CT47^2T6 1974 191037550 Power N-CT47^2T5 2021 192160336 Power N-CT47^2T4 2068 192632728 Power N-CT47^2T3 2115 192968122 Power N-CT47^2T2 2209 193026442 Power N-CT47^2 2211 194127934 Power N-CT47^2+2 2212 202458118 Add 1 factors 2213 205813462 Add 2 factors 2218 207324706 Add 9 factors 2220 208426198 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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