Table for CAN(6,k,12) 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,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 3546657 Augment OA 9 3859296 Augment OA 10 4191958 Augment OA 11 4542844 Augment OA 14 4826807 orthogonal array fuse 15 8225568 extended OA (Colbourn) special fuse 16 11985720 Add 1 factors 17 15131651 Add 3 factors 18 18559320 Add 3 factors 19 21549973 Martirosyan-TVT variant 20 21641253 Martirosyan-TVT 21 22018504 Martirosyan-TVT variant 22 22077142 Martirosyan-TVT 23 22640650 Martirosyan-TVT variant 26 22648871 double OA (Colbourn-Zhou) fuse 27 22949606 Martirosyan-TVT variant 28 23017967 double OA (Colbourn-Zhou) fuse 29 32839163 Add 1 factors 30 39151403 Add 2 factors 31 43808363 Add 3 factors 32 51240496 Add 5 factors 33 51347324 Add 5 factors 34 53075452 Add 13 factors 35 53337982 Add 13 factors 36 53901490 Add 13 factors 38 54268667 Add 13 factors 39 57240467 Add 13 factors 40 57620294 Add 13 factors 41 57733895 Add 13 factors 42 67792367 Add 13 factors 43 72402090 perfect hash family15,43,14 46 76261385 perfect hash family16,66,14T5 50 76594047 perfect hash family16,65,13T3 55 76944933 perfect hash family16,65,13T2 65 77228747 perfect hash family16,65,13,c fuse 66 77228896 perfect hash family16,66,14 67 92308444 Add 1 factors 68 99263788 Add 2 factors 69 104738092 Add 3 factors 70 111016538 perfect hash family23,70,14 71 112558367 Add 5 factors 72 115275267 Add 6 factors 76 116043312 perfect hash family17,120,15S7 81 119442073 perfect hash family17,120,15S6 86 122840834 perfect hash family17,120,15S5 92 126239595 perfect hash family17,120,15S4 112 127341287 Power CT16^2Arc(18):9 twos,0 ones 120 131609072 Power CT16^2Arc(16) 121 135369224 Power CT16^2Arc(15) 123 139129376 Power CT16^2Arc(14) 126 142889528 Power CT16^2Arc(13) 130 146649680 Power CT16^2Arc(12) 135 150409832 Power CT16^2Arc(11) 141 154169984 Power CT16^2Arc(10) 148 157930136 Power CT16^2Arc(9) 156 161690288 Power CT16^2Arc(8) 165 165450440 Power CT16^2Arc(7) 175 169210592 Power CT16^2Arc(6) 186 172970744 Power CT16^2Arc(5) 198 176730896 Power CT16^2Arc(4) 211 180491048 Power CT16^2Arc(3) 225 184251200 Power CT16^2T1T1 240 188011352 Power CT16^2T1 256 191771504 Power CT16^2 257 218383496 Add 1 factors 258 229826312 Add 2 factors 259 236365064 Add 3 factors 272 238960469 Power CT17^2T1 289 242106400 Power CT17^2 290 269350012 Add 1 factors 291 280792828 Add 2 factors 292 287711740 Add 3 factors 294 296331726 Add 5 factors 295 300353200 Add 6 factors 296 305911347 Martirosyan-TVT 302 307118464 Add 13 factors 312 309671499 Martirosyan-TVT 330 313433884 Martirosyan-TVT 338 317194036 Martirosyan-TVT 339 318177601 Martirosyan-TVT variant 340 319415647 Martirosyan-TVT 342 325791379 Martirosyan-TVT 344 331157971 Martirosyan-TVT 346 333667027 Martirosyan-TVT 348 336868093 Martirosyan-TVT 350 337287358 Martirosyan-TVT 360 343892776 Power N-CT29^2T9S14 379 344270027 Power N-CT29^2T8S14 395 344328665 Power N-CT29^2T7S14 413 344892173 Power N-CT29^2T6S14 466 344900394 Power N-CT29^2T3S14 484 345201129 Power N-CT29^2T2S14 511 345269490 Power N-CT29^2Arc(15) 526 355090686 Power N-CT29^2Arc(14) 550 361810191 Power CT25^2T3 575 362373699 Power CT25^2T2 626 362381920 Power CT25^2+1 627 365990740 Power CT27^2Arc(4) 651 366291475 Power CT27^2Arc(3) 676 366592210 Power CT27^2T1T1 702 366892945 Power CT27^2T1 729 367193680 Power CT27^2 730 368287456 Power CT27^2+1 731 403953592 Add 1 factors 732 418342648 Add 2 factors 733 426478072 Add 3 factors 734 434554150 Add 5 factors 735 435696326 Add 5 factors 736 440607837 Add 6 factors 742 447566284 Add 13 factors 743 448712788 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 528327486 Add 1 factors 843 543174318 Add 2 factors 844 551385774 Add 3 factors 846 560666123 Add 5 factors 847 565677912 Add 6 factors 854 573791670 Add 13 factors 855 609706626 Add 1 factors 856 624553458 Add 2 factors 857 632764914 Add 3 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 693083682 Add 1 factors 963 707947938 Add 2 factors 964 716159394 Add 3 factors 966 725441316 Add 5 factors 967 730461562 Add 6 factors 974 738609846 Add 13 factors 990 752746948 Martirosyan-TVT 991 752884708 Martirosyan-TVT variant 1012 753022468 Martirosyan-TVT 1022 753268846 Martirosyan-TVT 1052 763090042 Martirosyan-TVT 1058 769809547 Martirosyan-TVT 1064 770093360 Power N-CT41^2T13T3 1100 772717309 Martirosyan-TVT 1106 773280817 Martirosyan-TVT 1148 773294171 Martirosyan-TVT 1150 773352735 Martirosyan-TVT 1170 773360956 Martirosyan-TVT 1171 776270296 Martirosyan-TVT variant 1192 779179636 Martirosyan-TVT 1204 784965856 Martirosyan-TVT 1205 785919424 Martirosyan-TVT variant 1228 786890416 Martirosyan-TVT 1230 789692024 Power N-CT41^2T11 1240 794235383 Power N-CT41^2T10T1 1271 794348984 Power N-CT41^2T10 1339 797878832 Power N-CT41^2Trin3,3,3 1374 800850632 Power N-CT41^2Trin2,3,3 1409 801230459 Power N-CT41^2Trin1,3,3 1444 801344060 Power N-CT41^2T3T3 1446 804202259 Power N-CT41^2Trin1,2,3 1482 804315860 Power N-CT41^2T3T2 1483 804582086 Power N-CT41^2Arc(2)T3 1520 804695687 Power N-CT41^2T3T1 1558 804809288 Power N-CT41^2T3 1560 807667487 Power N-CT41^2T2T1 1599 807781088 Power N-CT41^2T2 1600 808047314 Power N-CT41^2T1T1 1640 808160915 Power N-CT41^2T1 1681 808274516 Power N-CT41^2 1682 847110896 Add 1 factors 1683 863234432 Add 2 factors 1684 871807040 Add 3 factors 1686 881301295 Add 5 factors 1687 886671569 Add 6 factors 1694 895273532 Add 13 factors 1695 934109912 Add 13 factors 1696 950233448 Add 13 factors 1697 958806056 Add 13 factors 1699 968300311 Add 13 factors 1700 973670585 Add 13 factors 1707 982272548 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 1053456492 Power N-CT47^2T6 2014 1054552782 Power N-CT53^2T15 2074 1057049149 Power N-CT61^2T27 2135 1057311679 Power N-CT61^2T26 2196 1057875187 Power N-CT61^2T25 2318 1058242364 Power N-CT61^2T23 2379 1061214164 Power N-CT61^2T22 2440 1061593991 Power N-CT61^2T21 2501 1061707592 Power N-CT61^2T20 2562 1071766064 Power N-CT61^2T19 2623 1076375787 Power N-CT61^2T18 2650 1076878162 Power N-CT53^2T3 2811 1077229048 Power N-CT53^2+2 2821 1080351002 Power N-CT59^2Trin4,4,4 3050 1080567744 Power N-CT61^2T11 3355 1080918630 Power N-CT61^2T6 3724 1081202444 Power N-CT61^2+3 3751 1111363626 Power N-CT67^2Arc(12) 3807 1126443174 Power N-CT67^2Arc(11) 3864 1141522722 Power N-CT67^2Arc(10) 3922 1156602270 Power N-CT67^2Arc(9) 3981 1171681818 Power N-CT67^2Arc(8) 5040 1179368866 Power CT31^3T17S30 5400 1182767627 Power CT31^3T16S30 5758 1186527779 Power CT31^3T15S30 6119 1189673710 Power CT31^3T14S30 6477 1193101379 Power CT31^3T13S30 6837 1196092032 Power CT31^3T12S30 7197 1196183312 Power CT31^3T11S30 7555 1196560563 Power CT31^3T10S30 7915 1196619201 Power CT31^3T9S30 8275 1197182709 Power CT31^3T8S30 9351 1197190930 Power CT31^3T5S30 9711 1197491665 Power CT31^3T4S30 10000 1197560026 Power CT31^3T3S30

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