Table for CAN(6,k,12) 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,12) 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 2985984 composition 8 3553567 Add a symbol 9 3876618 Add a symbol 10 4229037 Add a symbol 11 4613494 Add a symbol 14 4826807 orthogonal array fuse 15 8586563 Add 1 factors 16 12017507 Add 2 factors 17 15134819 Add 3 factors 18 18920315 Add 3 factors 20 21734608 Martirosyan-Tran van Trung 22 22179659 Martirosyan-Tran van Trung 26 22648871 double OA (Colbourn-Zhou) fuse 28 23017967 double OA (Colbourn-Zhou) fuse 29 32839163 Add 1 factors 30 39151403 Add 2 factors 31 43808363 Add 3 factors 32 51733408 Add 13 factors 33 52433224 Add 13 factors 34 53236607 Add 13 factors 35 53440499 Add 13 factors 36 53909711 Add 13 factors 38 54270695 Add 13 factors 39 57247955 Add 13 factors 40 57696143 Add 13 factors 41 57733895 Add 13 factors 42 67792367 Add 13 factors 43 72402090 perfect hash family15,43,14 46 76278707 perfect hash family16,66,14T5 50 76631126 perfect hash family16,65,13T3 55 77015583 perfect hash family16,65,13T2 65 77228747 perfect hash family16,65,13,c fuse 66 77228896 perfect hash family16,66,14 67 92743120 Add 1 factors 68 99698464 Add 2 factors 69 105172768 Add 3 factors 70 111016538 perfect hash family23,70,14 71 115893506 perfect hash family17,120,15S8 76 119653262 perfect hash family17,120,15S7 78 120629819 Add 13 factors 79 120629968 Add 13 factors 81 123413018 perfect hash family17,120,15S6 86 127172774 perfect hash family17,120,15S5 112 127563796 Power CT16^2Arc(18):9 twos,0 ones 113 135083308 Power CT16^2Arc(18):7 twos,2 ones 120 137384992 Power CT16^2Arc(16) 121 140815936 Power CT16^2Arc(15) 123 144246880 Power CT16^2Arc(14) 126 147677824 Power CT16^2Arc(13) 127 150122332 Power CT16^2Arc(18):3 twos,6 ones 130 151108768 Power CT16^2Arc(12) 131 153224464 Power CT16^2Arc(14):4 twos,3 ones 132 153553276 Power CT16^2Arc(16):3 twos,5 ones 133 153882088 Power CT16^2Arc(18):2 twos,7 ones 135 154539712 Power CT16^2Arc(11) 136 156326596 Power CT16^2TD(4):2,2,2,2,2 137 156655408 Power CT16^2Arc(12):4 twos,2 ones 138 156984220 Power CT16^2Arc(14):3 twos,4 ones 139 157313032 Power CT16^2Arc(16):2 twos,6 ones 140 157641844 Power CT16^2Arc(18):1 twos,8 ones 141 157970656 Power CT16^2Arc(10) 144 160086352 Power CT16^2TD(4):2,2,2,2,1 145 160415164 Power CT16^2Arc(12):3 twos,3 ones 146 160743976 Power CT16^2Arc(14):2 twos,5 ones 147 161072788 Power CT16^2Arc(16):1 twos,7 ones 148 161401600 Power CT16^2Arc(9) 152 163517296 Power CT16^2TD(4):2,2,2,2,0 153 163846108 Power CT16^2TD(4):2,2,2,1,1 154 164174920 Power CT16^2Arc(12):2 twos,4 ones 155 164503732 Power CT16^2Arc(14):1 twos,6 ones 156 164832544 Power CT16^2Arc(8) 162 167277052 Power CT16^2TD(4):2,2,2,1,0 163 167605864 Power CT16^2TD(4):2,2,1,1,1 164 167934676 Power CT16^2Arc(5)T2 165 168263488 Power CT16^2Arc(7) 172 170707996 Power CT16^2TD(2):2,2,2 173 171036808 Power CT16^2TD(4):2,2,1,1,0 174 171365620 Power CT16^2Arc(4)T2 175 171694432 Power CT16^2Arc(6) 184 174467752 Power CT16^2TD(2):1,2,2 185 174796564 Power CT16^2Arc(3)T2 186 175125376 Power CT16^2Arc(5) 196 177898696 Power CT16^2T2T2 197 178227508 Power CT16^2Arc(2)T2 198 178556320 Power CT16^2Arc(4) 210 181658452 Power CT16^2T2T1 211 181987264 Power CT16^2Arc(3) 224 185089396 Power CT16^2T2 225 185418208 Power CT16^2T1T1 240 188849152 Power CT16^2T1 256 192280096 Power CT16^2 257 218892088 Add 1 factors 258 230334904 Add 2 factors 259 236873656 Add 3 factors 272 239039776 Power CT17^2T1 289 242157088 Power CT17^2 290 269400700 Add 1 factors 291 280843516 Add 2 factors 292 287762428 Add 3 factors 293 302713636 Add 4 factors 294 305328327 Add 5 factors 302 307169152 Add 13 factors 304 311525666 Martirosyan-Tran van Trung 306 311854478 Martirosyan-Tran van Trung 308 312183290 Martirosyan-Tran van Trung 310 312512102 Martirosyan-Tran van Trung 312 312840914 Martirosyan-Tran van Trung 324 315285422 Martirosyan-Tran van Trung 326 315614234 Martirosyan-Tran van Trung 328 315943046 Martirosyan-Tran van Trung 330 316271858 Martirosyan-Tran van Trung 338 318716366 Martirosyan-Tran van Trung 340 320931297 Martirosyan-Tran van Trung 342 327307029 Martirosyan-Tran van Trung 344 332673621 Martirosyan-Tran van Trung 346 335511489 Martirosyan-Tran van Trung 348 341897781 Martirosyan-Tran van Trung 350 343572564 Martirosyan-Tran van Trung 360 343986131 Power N-CT29^2T9S14 395 344431182 Power N-CT29^2T7S14 466 344900394 Power N-CT29^2T3S14 511 345269490 Power N-CT29^2Arc(15) 526 355090686 Power N-CT29^2Arc(14) 550 361912708 Power CT25^2T3 626 362381920 Power CT25^2+1 627 366811072 Power CT27^2Arc(4) 651 367180168 Power CT27^2Arc(3) 676 367549264 Power CT27^2T1T1 702 367918360 Power CT27^2T1 730 368287456 Power CT27^2+1 731 404193832 Add 1 factors 732 418582888 Add 2 factors 733 426718312 Add 3 factors 734 444541192 Add 4 factors 735 447155883 Add 5 factors 742 448943980 Add 13 factors 743 448996708 Add 13 factors 757 463123842 Power N-CT29^2Arc(3) 784 472945038 Power N-CT29^2T1T1 812 482766234 Power N-CT29^2T1 841 492587430 Power N-CT29^2 842 528835422 Add 1 factors 843 543685422 Add 2 factors 844 551896878 Add 3 factors 845 569940498 Add 4 factors 846 572555189 Add 5 factors 854 574396014 Add 13 factors 855 610644006 Add 13 factors 856 625494006 Add 13 factors 857 633705462 Add 13 factors 868 636335034 Power N-CT31^2T3 870 641499270 Power N-CT31^2T2T1 871 643154550 Power N-CT31^2Arc(3) 899 646156230 Power N-CT31^2T2 900 647811510 Power N-CT31^2T1T1 930 652468470 Power N-CT31^2T1 961 657125430 Power N-CT31^2 962 693883734 Add 1 factors 963 708751158 Add 2 factors 964 716962614 Add 3 factors 965 735103902 Add 4 factors 966 737718593 Add 5 factors 968 739272066 Add 13 factors 974 739559418 Add 13 factors 1012 764693981 Martirosyan-Tran van Trung 1014 765118746 Martirosyan-Tran van Trung 1022 767758026 Martirosyan-Tran van Trung 1039 770057636 Power N-CT41^2Trin1,3,13 1064 770095388 Power N-CT41^2T13T3 1066 773034896 Power N-CT41^2Trin1,2,13 1092 773072648 Power N-CT41^2T13T2 1093 773483084 Power N-CT41^2Arc(2)T13 1120 773520836 Power N-CT41^2T13T1 1148 773558588 Power N-CT41^2T13 1160 783342032 Power N-CT41^2T12T1 1189 783379784 Power N-CT41^2T12 1200 789654272 Power N-CT41^2T11T1 1230 789692024 Power N-CT41^2T11 1240 794311232 Power N-CT41^2T10T1 1271 794348984 Power N-CT41^2T10 1339 797884916 Power N-CT41^2Trin3,3,3 1374 800862176 Power N-CT41^2Trin2,3,3 1409 801310364 Power N-CT41^2Trin1,3,3 1444 801348116 Power N-CT41^2T3T3 1446 804287624 Power N-CT41^2Trin1,2,3 1482 804325376 Power N-CT41^2T3T2 1483 804735812 Power N-CT41^2Arc(2)T3 1520 804773564 Power N-CT41^2T3T1 1558 804811316 Power N-CT41^2T3 1560 807750824 Power N-CT41^2T2T1 1599 807788576 Power N-CT41^2T2 1600 808199012 Power N-CT41^2T1T1 1640 808236764 Power N-CT41^2T1 1681 808274516 Power N-CT41^2 1682 847110896 Add 1 factors 1683 863237600 Add 2 factors 1684 871810208 Add 3 factors 1685 890822072 Add 4 factors 1686 893436763 Add 5 factors 1694 895277588 Add 13 factors 1695 934113968 Add 13 factors 1696 950240672 Add 13 factors 1697 958813280 Add 13 factors 1698 977825144 Add 13 factors 1699 980439835 Add 13 factors 1707 982280660 Add 13 factors 1722 994351328 Power N-CT43^2T2T1 1763 998961051 Power N-CT43^2T2 1764 1004409800 Power N-CT43^2T1T1 1806 1009019523 Power N-CT43^2T1 1849 1013629246 Power N-CT43^2 1891 1047782060 Power N-CT61^2T30 1927 1053938519 Power N-CT47^2T6 2014 1055473260 Power N-CT53^2T15 2074 1057210304 Power N-CT61^2T27 2135 1057414196 Power N-CT61^2T26 2196 1057883408 Power N-CT61^2T25 2318 1058244392 Power N-CT61^2T23 2379 1061221652 Power N-CT61^2T22 2440 1061669840 Power N-CT61^2T21 2501 1061707592 Power N-CT61^2T20 2562 1071766064 Power N-CT61^2T19 2623 1076375787 Power N-CT61^2T18 2650 1077833691 Power N-CT53^2T3 2811 1078218148 Power N-CT53^2+2 2821 1080562952 Power N-CT59^2Trin4,4,4 3050 1080604823 Power N-CT61^2T11 3355 1080989280 Power N-CT61^2T6 3724 1081202444 Power N-CT61^2+3 3751 1112232978 Power N-CT67^2Arc(12) 3807 1127747202 Power N-CT67^2Arc(11) 3864 1143261426 Power N-CT67^2Arc(10) 3922 1158775650 Power N-CT67^2Arc(9) 3981 1174289874 Power N-CT67^2Arc(8) 5040 1179368866 Power CT31^3T17S30 5400 1183128622 Power CT31^3T16S30 5758 1186559566 Power CT31^3T15S30 6119 1189676878 Power CT31^3T14S30 6477 1193462374 Power CT31^3T13S30 7197 1196276667 Power CT31^3T11S30 7915 1196721718 Power CT31^3T9S30 9351 1197190930 Power CT31^3T5S30 10000 1197560026 Power CT31^3T3S30

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