Table for CAN(6,k,7) 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,7) 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 8 117649 orthogonal array 9 216090 extended OA (Colbourn) 10 316932 Add 1 factors 11 417774 Add 2 factors 12 518616 Add 3 factors 14 521017 double OA (Colbourn-Zhou) 16 537481 double OA (Colbourn-Zhou) 17 738871 Add 1 factors 18 926149 Add 2 factors 19 1088731 Add 3 factors 20 1189573 Add 4 factors 21 1257487 Add 7 factors 22 1284241 Add 7 factors 23 1290415 Add 7 factors 24 1497979 Add 7 factors 25 1697605 Add 7 factors 26 1866361 Add 7 factors 28 2044588 Martirosyan-Tran van Trung 30 2089822 Martirosyan-Tran van Trung 32 2118592 Martirosyan-Tran van Trung 34 2467900 Martirosyan-Tran van Trung 36 2728306 Martirosyan-Tran van Trung 37 2974174 Add 7 factors 38 3009118 Add 7 factors 39 3109666 Add 7 factors 40 3458974 Add 7 factors 41 3460738 Add 7 factors 43 3721144 Add 7 factors 44 3852590 Martirosyan-Tran van Trung 46 3878434 Martirosyan-Tran van Trung 48 4183936 Martirosyan-Tran van Trung 50 4438504 Martirosyan-Tran van Trung 52 4612552 Martirosyan-Tran van Trung 53 4871272 Add 7 factors 56 4913419 Martirosyan-Tran van Trung 58 4981585 Martirosyan-Tran van Trung 60 5024719 Martirosyan-Tran van Trung 64 5512129 Martirosyan-Tran van Trung 68 6003595 Martirosyan-Tran van Trung 72 6332803 Martirosyan-Tran van Trung 74 6673003 Martirosyan-Tran van Trung 76 6707947 Martirosyan-Tran van Trung 78 6981115 Martirosyan-Tran van Trung 80 7387255 Martirosyan-Tran van Trung 82 7738585 Martirosyan-Tran van Trung 84 7841471 Martirosyan-Tran van Trung 86 7864008 Martirosyan-Tran van Trung 88 7887041 Martirosyan-Tran van Trung 92 7918177 Martirosyan-Tran van Trung 100 8146920 Power CT16^2TD(2):2,2,8 112 8163384 Power CT16^2T8T2 128 8179848 Power CT16^2T8 144 8278289 Power CT16^2T7 160 8379131 Power CT16^2T6 176 8479973 Power CT16^2T5 196 8566752 Power CT16^2T2T2 224 8583216 Power CT16^2T2 256 8599680 Power CT16^2 257 9520530 Add 1 factors 258 9968880 Add 2 factors 259 10242594 Add 3 factors 260 10343436 Add 4 factors 263 10444278 Add 7 factors 264 11365128 Add 7 factors 272 11620530 Power CT17^2T1 289 11821920 Power CT17^2 290 12742770 Add 1 factors 291 13191120 Add 2 factors 292 13464834 Add 3 factors 293 13565676 Add 4 factors 296 13666518 Add 7 factors 297 14587368 Add 7 factors 298 15035718 Add 7 factors 299 15309432 Add 7 factors 300 15410274 Add 7 factors 303 15511116 Add 7 factors 304 16431966 Add 7 factors 305 16880316 Add 7 factors 306 16907238 Power CT19^2T2T1 307 16931934 Power CT19^2Arc(3) 320 16978811 perfect hash family32,512,16T6 323 17069820 Power CT19^2T2 352 17079653 perfect hash family32,512,16T5 384 17180495 perfect hash family32,512,16T4 448 17182896 perfect hash family32,512,16T2 512 17199360 perfect hash family32,512,16 513 18496572 Add 1 factors 514 19048410 Add 2 factors 515 19336530 Add 3 factors 516 19437372 Add 4 factors 519 19538214 Add 7 factors 529 20646624 Power CT23^2 530 21943836 Add 1 factors 531 22508316 Add 2 factors 532 22802610 Add 3 factors 533 22903452 Add 4 factors 536 23004294 Add 7 factors 537 24178992 Add 8 factors 544 24856443 Martirosyan-Tran van Trung 578 25102191 Martirosyan-Tran van Trung 579 26551359 Add 1 factors 600 26962038 Power CT25^2T1 625 27161664 Power CT25^2 626 28610832 Add 1 factors 627 29235876 Add 2 factors 628 29534286 Add 3 factors 629 29635128 Add 4 factors 632 29735970 Add 7 factors 640 30351728 Martirosyan-Tran van Trung 646 30442737 Martirosyan-Tran van Trung 686 30496928 Martirosyan-Tran van Trung 700 30665838 Martirosyan-Tran van Trung 704 30759736 Martirosyan-Tran van Trung 722 30860578 Martirosyan-Tran van Trung 725 30955098 Power N-CT29^2T4 728 31078620 Power N-CT29^2T3T1 754 31123854 Power N-CT29^2T3 757 31211613 Power N-CT29^2Arc(3) 784 31256847 Power N-CT29^2T1T1 812 31302081 Power N-CT29^2T1 842 31347315 Power N-CT29^2+1 843 31663785 Power N-CT31^2Arc(4) 871 31692555 Power N-CT31^2Arc(3) 900 31721325 Power N-CT31^2T1T1 930 31750095 Power N-CT31^2T1 962 31778865 Power N-CT31^2+1 963 33439125 Add 1 factors 1024 33897456 Power CT32^2 1025 35575314 Add 1 factors 1026 36258570 Add 2 factors 1027 36600198 Add 3 factors 1028 36701040 Add 4 factors 1031 36801882 Add 7 factors 1032 38200776 Add 8 factors 1036 39057640 Martirosyan-Tran van Trung 1038 39144076 Martirosyan-Tran van Trung 1042 40252486 Martirosyan-Tran van Trung 1052 40437802 Martirosyan-Tran van Trung 1058 40445740 Martirosyan-Tran van Trung 1059 42132418 Add 1 factors 1072 42399783 Power N-CT37^2Arc(9) 1101 42645651 Power N-CT37^2Arc(8) 1131 42891519 Power N-CT37^2Arc(7) 1162 43137387 Power N-CT37^2Arc(6) 1194 43383255 Power N-CT37^2Arc(5) 1227 43629123 Power N-CT37^2Arc(4) 1261 43874991 Power N-CT37^2Arc(3) 1296 44120859 Power N-CT37^2T1T1 1332 44366727 Power N-CT37^2T1 1369 44612595 Power N-CT37^2 1370 45136755 Power N-CT37^2+1 1371 46644975 Power N-CT37^2+2 1374 47196006 Power N-CT41^2Trin2,3,3 1410 47296554 Power N-CT41^2Trin2,2,3 1447 47397102 Power N-CT41^2Trin2,2,2 1482 47647626 Power N-CT41^2T3T2 1484 47746410 Power N-CT41^2Trin1,2,2 1521 47748174 Power N-CT41^2T2T2 1558 47998698 Power N-CT41^2T3 1560 48097482 Power N-CT41^2T2T1 1599 48099246 Power N-CT41^2T2 1600 48446790 Power N-CT41^2T1T1 1640 48448554 Power N-CT41^2T1 1681 48450318 Power N-CT41^2 1682 50254974 Add 1 factors 1683 50952342 Add 2 factors 1684 51306318 Add 3 factors 1685 51407160 Add 4 factors 1688 51508002 Add 7 factors 1720 51833832 Power N-CT43^2T3 1763 51835596 Power N-CT43^2T2 1849 52096002 Power N-CT43^2 1850 53919768 Add 1 factors 1852 54298062 Power N-CT43^2+3 1853 55079892 Add 4 factors 1856 55180734 Add 7 factors 1861 56131074 Power N-CT47^2Arc(8) 1901 56436576 Power N-CT47^2Arc(7) 1942 56742078 Power N-CT47^2Arc(6) 1984 57047580 Power N-CT47^2Arc(5) 2027 57353082 Power N-CT47^2Arc(4) 2071 57658584 Power N-CT47^2Arc(3) 2116 57964086 Power N-CT47^2T1T1 2162 58269588 Power N-CT47^2T1 2210 58575090 Power N-CT47^2+1 2211 60398856 Add 1 factors 2304 60611597 Power CT31^3T22T15T15 2560 60712439 Power CT31^3T21T15T15 2816 60813281 Power CT31^3T20T15T15 3136 60900060 Power CT31^3T17T17T15 3584 60916524 Power CT31^3T17T15T15 4096 60932988 Power CT31^3T15T15T15 4352 61134378 Power CT31^3T15T15T14 4608 61321656 Power CT31^3T15T15T13 4624 61335768 Power CT31^3T15T14T14 4864 61484238 Power CT31^3T15T15T12 4896 61523046 Power CT31^3T15T14T13 4913 61537158 Power CT31^3T14T14T14 5120 61585080 Power CT31^3T15T15T11 5376 61652994 Power CT31^3T15T15T10 5632 61679748 Power CT31^3T15T15T9 5888 61685922 Power CT31^3T15T15T8 5984 61881138 Power CT31^3T15T14T9 6256 61887312 Power CT31^3T15T14T8 6336 62068416 Power CT31^3T15T13T9 6624 62074590 Power CT31^3T15T13T8 6647 62088702 Power CT31^3T14T14T8 6688 62230998 Power CT31^3T15T12T9 6992 62237172 Power CT31^3T15T12T8 7038 62275980 Power CT31^3T14T13T8 7040 62331840 Power CT31^3T15T11T9 7360 62338014 Power CT31^3T15T11T8 7392 62399754 Power CT31^3T15T10T9 7728 62405928 Power CT31^3T15T10T8 7744 62426508 Power CT31^3T15T9T9 8096 62432682 Power CT31^3T15T9T8 8464 62438856 Power CT31^3T15T8T8 8602 62634072 Power CT31^3T14T9T8 8993 62640246 Power CT31^3T14T8T8 9108 62821350 Power CT31^3T13T9T8 9522 62827524 Power CT31^3T13T8T8 9614 62983932 Power CT31^3T12T9T8 10000 62990106 Power CT31^3T12T8T8

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