# Table for CAN(6,k,19) for k up to 10000

#### 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,19) 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 20 47045881 orthogonal array 21 91485342 extended OA (Colbourn) 22 136055124 Add 1 factors 24 148035881 orthogonal array fuse fuse fuse fuse 25 188183467 perfect hash family4,25,19,c 27 188183520 perfect hash family4,27,20 38 225325009 double OA (Colbourn-Zhou) 40 227794249 double OA (Colbourn-Zhou) 41 359028199 Add 1 factors 42 423412777 perfect hash family9,42,19,c 45 423412920 perfect hash family9,45,20 47 470458639 perfect hash family10,47,19,c 51 470458800 perfect hash family10,51,20 53 517504501 perfect hash family11,53,19,c 60 517504680 perfect hash family11,60,20 64 564550560 perfect hash family12,64,20 65 658642320 perfect hash family14,65,20 95 705687949 perfect hash family15,95,19,c 96 705688200 perfect hash family15,96,20 361 752733811 perfect hash family16,361,19,c 362 752734080 Power CT19^2+1 363 968422194 Add 1 factors 364 1057555260 Add 2 factors 365 1144349046 Add 3 factors 366 1188918828 Add 4 factors 380 1233488341 Add 19 factors 381 1233488610 Add 19 factors 382 1473622200 Add 19 factors 515 1505467603 perfect hash family32,515,19,c 516 1505468160 perfect hash family32,516,20 517 1850044446 Add 1 factors 518 2008108296 Add 2 factors 519 2070018720 perfect hash family44,519,20 520 2117063809 perfect hash family45,520,19,c 522 2117064600 perfect hash family45,522,20 523 2199350377 Add 19 factors 525 2199597301 Add 19 factors 529 2199720763 Add 19 factors 532 2199844225 Add 19 factors 534 2199967687 Add 19 factors 535 2199968244 Add 19 factors 722 2273305342 Martirosyan-TVT 723 2323554645 Martirosyan-TVT variant 724 2373803679 Martirosyan-TVT 726 2673933645 Martirosyan-TVT 728 2845292403 Martirosyan-TVT 730 2974310193 Martirosyan-TVT 734 2996903470 Add 19 factors 739 2997026932 Add 19 factors 741 2997150394 Add 19 factors 742 3047399697 Add 19 factors 760 3105673492 Martirosyan-TVT 808 3149508743 Power N-CT41^2T14S13 1134 3186650232 Power N-CT41^2T3S13 1198 3189119472 Power N-CT41^2Arc(14) 1226 3320353422 Power N-CT41^2Arc(13) 1370 3379875120 Power N-CT37^2+1 1372 3416913720 Power N-CT37^2+3 1373 3885939702 Add 1 factors 1381 3976523172 Power N-CT41^2Arc(8) 1415 4107757122 Power N-CT41^2Arc(7) 1450 4238991072 Power N-CT41^2Arc(6) 1486 4370225022 Power N-CT41^2Arc(5) 1523 4501458972 Power N-CT41^2Arc(4) 1561 4632692922 Power N-CT41^2Arc(3) 1600 4763926872 Power N-CT41^2T1T1 1640 4895160822 Power N-CT41^2T1 1681 5026394772 Power N-CT41^2 1682 5495420754 Add 1 factors 1683 5709003516 Add 2 factors 1720 5732162195 Power N-CT43^2T3 1722 5863396002 Power N-CT43^2T2T1 1763 5863396145 Power N-CT43^2T2 1764 5927780580 Power N-CT43^2T1T1 1806 5927780723 Power N-CT43^2T1 1851 5927780866 Power N-CT43^2+2 1880 6343756542 Power N-CT47^2T7 1939 6445283775 Power N-CT47^2Trin2,2,2 8000 6450237864 Power CT31^3T11T11T11 8400 6494677325 Power CT31^3T11T11T10 8820 6539116786 Power CT31^3T11T10T10 9600 6551227864 Power CT31^3T11T11T7 10000 6591375450 Power CT31^3T11T11T6
Graph: