Table for CAN(6,k,23) for k up to 10000

Last Updated Wed Mar 9 06:22:05 MST 2022

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,23) 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 24 148035889 orthogonal array 26 244140621 orthogonal array fuse fuse 28 387420481 orthogonal array fuse fuse fuse fuse 29 443827803 4-Restricted SCPHF RE (CL) 30 444107115 2-Restricted SCPHF RE (CL) 31 444107621 SCPHF Random Extension (CLS) 34 444107665 CPHF IPO 3 (WCS) 41 579270847 5,5-Restricted SCPHF RE (CL) 45 585707167 5-Restricted SCPHF RE (CL) 51 591863669 4-Restricted SCPHF RE (CL) 52 592142981 2-Restricted SCPHF RE (CL) 70 727306713 5,5-Restricted SCPHF RE (CL) 78 733743033 5-Restricted SCPHF RE (CL) 85 739899535 4-Restricted SCPHF RE (CL) 87 740167209 3-Restricted SCPHF RE (CL) 106 868906259 5,5,5-Restricted SCPHF RE (CL) 119 875342579 5,5-Restricted SCPHF RE (CL) 133 881778899 5-Restricted SCPHF RE (CL) 145 887935401 4-Restricted SCPHF RE (CL) 146 888214713 2-Restricted SCPHF RE (CL) 148 888215219 SCPHF Random Extension (CLS) 249 1036251085 SCPHF Random Extension (CLS) 250 1602647751 Add 1 factors 265 1708984221 SCPHF Random Extension (CLS) fuse fuse 266 2275380887 Add 1 factors 529 2368573879 perfect hash family16,529,23,c 530 2368574208 Power CT23^2+1 531 3057834758 Add 1 factors 532 3341022212 Add 2 factors 553 3617935724 Power CT25^2Arc(3) 576 3714040456 Power CT25^2T1T1 600 3810145188 Power CT25^2T1 625 3906249621 perfect hash family16,625,25,c fuse fuse 626 3906249920 Power CT25^2+1 627 4614245626 Add 1 factors 628 4977874936 Add 2 factors 629 5278740512 Add 3 factors 630 5420340058 Add 4 factors 634 5555749913 Add 23 factors 643 5556005949 Add 23 factors 648 5556050477 Add 23 factors 649 5561939604 Add 23 factors 651 5768888100 Power CT27^2Arc(3) 676 5912167960 Power CT27^2T1T1 702 6055447820 Power CT27^2T1 730 6198727680 Power CT27^2+1 735 6217506504 perfect hash family6,735,249 744 6365542568 Power N-CT31^2T7 754 6457729848 Power N-CT29^2T3 755 6461646288 Power N-CT31^2Arc(2)T5 780 6461646794 Power N-CT31^2T5T1 806 6461647300 Power N-CT31^2T5 812 6601009708 Power N-CT29^2T1 813 6604926148 Power N-CT31^2Arc(2)T3 840 6604926654 Power N-CT31^2T3T1 868 6604927160 Power N-CT31^2T3 870 6661333976 Power N-CT31^2T2T1 899 6661334482 Power N-CT31^2T2 900 6661613288 Power N-CT31^2T1T1 930 6661613794 Power N-CT31^2T1 961 6661614300 Power N-CT31^2 964 6661614960 Power N-CT31^2+3 986 6758182644 Martirosyan-TVT 1018 6764338640 Martirosyan-TVT 1019 6764873482 Martirosyan-TVT variant 1058 6765408808 Martirosyan-TVT 1059 6802592547 Martirosyan-TVT variant 1060 6839775957 Martirosyan-TVT 1062 7529036507 Martirosyan-TVT 1250 7731203449 perfect hash familyD16,1250,50^11 25^5 1271 7974628618 Power N-CT41^2T10 1394 7974628662 Power N-CT41^2T7 1462 8058300822 Power N-CT43^2T9 1681 8109791844 Power N-CT41^2 1763 8193464004 Power N-CT43^2T2 1851 8199900324 Power N-CT43^2+2 1939 8267621846 Power N-CT47^2Trin2,2,2 2025 8273778348 Power N-CT47^2T2T2 2115 8279934850 Power N-CT47^2T2 2213 8286091352 perfect hash family14,2213,51 2214 8290001720 perfect hash family14,2214,52 2239 8560329184 Power N-CT53^2Arc(12) 2281 8695492916 Power N-CT53^2Arc(11) 2324 8830656648 Power N-CT53^2Arc(10) 2368 8965820380 Power N-CT53^2Arc(9) 2413 9100984112 Power N-CT53^2Arc(8) 2459 9236147844 Power N-CT53^2Arc(7) 2514 9248464368 Power N-CT73^2Trin3,22,22 2562 9248743680 Power N-CT73^2Trin3,21,22 2611 9249022992 Power N-CT73^2Trin3,21,21 2652 9255180000 Power N-CT73^2T22T21 2704 9255459312 Power N-CT73^2T21T21 2822 9322902072 Power N-CT83^2T49 3024 9377750910 Power N-CT73^2Trin3,3,28 3426 9383907412 Power N-CT73^2Trin3,3,22 3493 9384186724 Power N-CT73^2Trin3,3,21 3570 9390343732 Power N-CT73^2T22T3 3640 9390623044 Power N-CT73^2T21T3 3723 9396780052 Power N-CT73^2T22 3796 9397059364 Power N-CT73^2T21 3811 9433998376 Power N-CT79^2Arc(6)T27 3858 9440154878 Power N-CT79^2Arc(5)T27 3906 9446311380 Power N-CT79^2Arc(4)T27 3955 9452467882 Power N-CT79^2Arc(3)T27 4005 9458624384 Power N-CT79^2Arc(2)T27 4056 9464780886 Power N-CT79^2T27T1 4233 9470658076 Power N-CT83^2T32 4316 9470937388 Power N-CT83^2T31 4699 9519350456 Power N-CT73^2Trin3,3,3 4900 9525786776 Power N-CT73^2T3T3 5110 9532223096 Power N-CT73^2T3 5334 9538659416 perfect hash family13,5334,78 5359 9544815918 Power N-CT79^2Arc(12) 5427 9550972420 Power N-CT79^2Arc(11) 5496 9557128922 Power N-CT79^2Arc(10) 5566 9563285424 Power N-CT79^2Arc(9) 5637 9569441926 Power N-CT79^2Arc(8) 5709 9575598428 Power N-CT79^2Arc(7) 5782 9581754930 Power N-CT79^2Arc(6) 5856 9587911432 Power N-CT79^2Arc(5) 5931 9594067934 Power N-CT79^2Arc(4) 6007 9600224436 Power N-CT79^2Arc(3) 6084 9606380938 Power N-CT79^2T1T1 6474 9612537440 Power N-CT83^2T5 6891 9618693942 Power N-CT83^2+2 6893 9622173704 perfect hash family13,6893,87 6901 10908761182 Power N-CT89^2Trin4,4,4 7063 10909028856 Power N-CT89^2Trin2,4,4 7229 10909296530 Power N-CT89^2Trin2,2,4 7399 10909564204 Power N-CT89^2Trin2,2,2 7569 11038303254 Power N-CT89^2T2T2 8034 11160618128 perfect hash family13,10609,103T25 8755 11166774630 perfect hash family13,10609,103T18 8961 11167042304 perfect hash family13,10609,103T16 9605 11244010470 perfect hash family13,12769,113T28 9831 11244278144 perfect hash family13,12769,113T26 10000 11295781354 Power N-CT101^2

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