Table for CAN(6,k,12) for k up to 10000

Last Updated Fri Mar 27 17:29:25 MST 2015

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).

Change t: - Change v: - + or go to Global Menu.

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 92740216 Add 1 factors 68 99695560 Add 2 factors 69 105169864 Add 3 factors 70 111016538 perfect hash family23,70,14 71 112644551 perfect hash family17,120,15S8 72 115716852 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 404193832 Add 1 factors 732 418582888 Add 2 factors 733 426718312 Add 3 factors 734 434794390 Add 5 factors 735 435936566 Add 5 factors 736 440853537 Add 6 factors 742 447850204 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 846 561177513 Add 5 factors 847 566201482 Add 6 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 693830802 Add 1 factors 963 708698226 Add 2 factors 964 716909682 Add 3 factors 966 726191890 Add 5 factors 967 731229752 Add 6 factors 968 739209510 Add 13 factors 974 739496862 Add 13 factors 1012 762769828 Martirosyan-TVT 1014 763016206 Martirosyan-TVT 1015 764324926 Martirosyan-TVT variant 1022 765633646 Martirosyan-TVT 1039 769979759 Power N-CT41^2Trin1,3,13 1064 770093360 Power N-CT41^2T13T3 1066 772951559 Power N-CT41^2Trin1,2,13 1092 773065160 Power N-CT41^2T13T2 1093 773331386 Power N-CT41^2Arc(2)T13 1120 773444987 Power N-CT41^2T13T1 1148 773558588 Power N-CT41^2T13 1160 783266183 Power N-CT41^2T12T1 1189 783379784 Power N-CT41^2T12 1200 789578423 Power N-CT41^2T11T1 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 863237600 Add 2 factors 1684 871810208 Add 3 factors 1686 881304749 Add 5 factors 1687 886675659 Add 6 factors 1694 895277588 Add 13 factors 1695 934113968 Add 13 factors 1696 950240672 Add 13 factors 1697 958813280 Add 13 factors 1699 968307821 Add 13 factors 1700 973678731 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 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 1112227170 Power N-CT67^2Arc(12) 3807 1127738490 Power N-CT67^2Arc(11) 3864 1143249810 Power N-CT67^2Arc(10) 3922 1158761130 Power N-CT67^2Arc(9) 3981 1174272450 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

Graph: