Table for CAN(6,k,18) 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,18) 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 34012224 composition 8 38131351 Add a symbol 9 40374371 Add a symbol 10 42749334 Add a symbol 11 45264000 Add a symbol 20 47045879 orthogonal array fuse 21 86923493 Add 1 factors 22 124686341 Add 2 factors 24 148035879 orthogonal array fuse fuse fuse fuse fuse 25 188183465 perfect hash family4,25,19,c fuse 27 188183512 perfect hash family4,27,20 38 225325007 double OA (Colbourn-Zhou) fuse 40 227794247 double OA (Colbourn-Zhou) fuse 41 336759011 Add 1 factors 42 408043547 Add 2 factors 45 423412902 perfect hash family9,45,20 47 470458637 perfect hash family10,47,19,c fuse 51 470458780 perfect hash family10,51,20 53 517504499 perfect hash family11,53,19,c fuse 60 517504658 perfect hash family11,60,20 64 564550536 perfect hash family12,64,20 65 658642292 perfect hash family14,65,20 95 705687947 perfect hash family15,95,19,c fuse 96 705688170 perfect hash family15,96,20 133 739700393 Power CT19^2T12 152 743819520 Power CT19^2T11 171 746062540 Power CT19^2T10 190 748437503 Power CT19^2T9 209 750952169 Power CT19^2T8 361 752733809 perfect hash family16,361,19,c fuse 362 752734048 Power CT19^2+1 363 945717538 Add 1 factors 364 1021259758 Add 2 factors 365 1124458024 Add 3 factors 366 1183966636 Add 4 factors 367 1215502761 Add 5 factors 380 1228536179 Add 19 factors 381 1228536418 Add 19 factors 382 1425247906 Add 1 factors 383 1500790126 Add 2 factors 515 1505467601 perfect hash family32,515,19,c fuse 516 1505468096 perfect hash family32,516,20 517 1803219254 Add 1 factors 518 1931908166 Add 2 factors 519 2066011406 Add 3 factors 520 2117063807 perfect hash family45,520,19,c fuse 522 2117064510 perfect hash family45,522,20 524 2170198637 Add 19 factors 531 2172297491 Add 19 factors 534 2172420953 Add 19 factors 535 2172421448 Add 19 factors 684 2220737084 Martirosyan-Tran van Trung 722 2221998414 Martirosyan-Tran van Trung 724 2238616265 Martirosyan-Tran van Trung 726 2502945185 Martirosyan-Tran van Trung 728 2642347157 Martirosyan-Tran van Trung 730 2795441171 Martirosyan-Tran van Trung 732 2892612263 Martirosyan-Tran van Trung 741 2908617450 Add 19 factors 742 2925235301 Add 19 factors 743 2929401887 Add 19 factors 760 2947152816 Martirosyan-Tran van Trung 762 2956429619 Martirosyan-Tran van Trung 808 3149508709 Power N-CT41^2T14S13 1134 3186650204 Power N-CT41^2T3S13 1198 3189119444 Power N-CT41^2Arc(14) 1226 3298084208 Power N-CT41^2Arc(13) 1370 3379875090 Power N-CT37^2+1 1372 3416913690 Power N-CT37^2+3 1373 3815910762 Add 1 factors 1381 3842908028 Power N-CT41^2Arc(8) 1415 3951872792 Power N-CT41^2Arc(7) 1450 4060837556 Power N-CT41^2Arc(6) 1486 4169802320 Power N-CT41^2Arc(5) 1523 4278767084 Power N-CT41^2Arc(4) 1561 4387731848 Power N-CT41^2Arc(3) 1600 4496696612 Power N-CT41^2T1T1 1640 4605661376 Power N-CT41^2T1 1681 4714626140 Power N-CT41^2 1682 5118489836 Add 1 factors 1683 5291094032 Add 2 factors 1684 5465001734 Add 3 factors 1685 5531860106 Add 4 factors 1686 5563396231 Add 5 factors 1700 5576429888 Add 19 factors 1720 5732161959 Power N-CT43^2T3 1722 5825757368 Power N-CT43^2T2T1 1763 5841126723 Power N-CT43^2T2 1764 5897041904 Power N-CT43^2T1T1 1806 5912411259 Power N-CT43^2T1 1851 5927780614 Power N-CT43^2+2 1852 6334542436 Add 1 factors 1880 6343756514 Power N-CT47^2T7 2800 6437204147 Power CT31^3T24T11T11 3200 6441323274 Power CT31^3T23T11T11 3600 6443566294 Power CT31^3T22T11T11 4000 6445941257 Power CT31^3T21T11T11 4400 6448455923 Power CT31^3T20T11T11 8000 6450237802 Power CT31^3T11T11T11 8400 6490115416 Power CT31^3T11T11T10 8800 6527878264 Power CT31^3T11T11T9 8820 6529993030 Power CT31^3T11T10T10 9600 6551227802 Power CT31^3T11T11T7 10000 6591105416 Power CT31^3T11T10T7

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