Table for CAN(6,k,13) 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,13) 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 14 4826809 orthogonal array 15 9253764 extended OA (Colbourn) 16 13709280 Add 1 factors 17 16777210 orthogonal array fuse fuse fuse 18 19307232 perfect hash family4,18,14 26 22648873 double OA (Colbourn-Zhou) 28 23017969 double OA (Colbourn-Zhou) 29 36013549 Add 1 factors 30 44581849 Add 2 factors 31 50652000 Add 13 factors 32 53094888 perfect hash family11,32,14 33 55074565 Add 13 factors 34 55390933 Add 13 factors 35 55707301 Add 13 factors 36 55944577 Add 13 factors 38 56181853 Add 13 factors 39 60189337 Add 13 factors 40 60584797 Add 13 factors 41 60901165 Add 13 factors 43 72402120 perfect hash family15,43,14 65 77228749 perfect hash family16,65,13,c 66 77228928 perfect hash family16,66,14 67 98451948 Add 1 factors 68 106189776 perfect hash family22,68,14 69 111016321 perfect hash family23,69,13,c 70 111016584 perfect hash family23,70,14 71 121898331 perfect hash family17,120,15S8 73 124815769 Add 13 factors 78 124840105 Add 13 factors 79 124840284 Add 13 factors 81 130752241 perfect hash family17,120,15S6 86 135179196 perfect hash family17,120,15S5 112 139406225 Power CT16^2Arc(18):9 twos,0 ones 120 148060208 Power CT16^2Arc(16) 121 152515724 Power CT16^2Arc(15) 123 156971240 Power CT16^2Arc(14) 126 161426756 Power CT16^2Arc(13) 130 165882272 Power CT16^2Arc(12) 135 170337788 Power CT16^2Arc(11) 141 174793304 Power CT16^2Arc(10) 148 179248820 Power CT16^2Arc(9) 156 183704336 Power CT16^2Arc(8) 165 188159852 Power CT16^2Arc(7) 175 192615368 Power CT16^2Arc(6) 186 197070884 Power CT16^2Arc(5) 198 201526400 Power CT16^2Arc(4) 211 205981916 Power CT16^2Arc(3) 225 210437432 Power CT16^2T1T1 240 214892948 Power CT16^2T1 256 219348464 Power CT16^2 257 251035964 Add 1 factors 272 265367414 Power CT17^2T1 289 268435344 Power CT17^2 290 301071948 Add 1 factors 291 317890152 Add 2 factors 292 328673028 Add 3 factors 293 333128544 Add 4 factors 296 335985635 Martirosyan-TVT 300 337267692 Add 13 factors 302 337584060 Add 13 factors 308 339028761 Power N-CT29^2T12S14 312 340441151 Martirosyan-TVT 325 341558783 Power N-CT29^2T11S14 350 344559888 Power CT25^2T11 466 344900424 Power N-CT29^2T3S14 511 345269520 Power N-CT29^2Arc(15) 526 358265100 Power N-CT29^2Arc(14) 626 362381952 Power CT25^2+1 627 366811104 Power CT27^2Arc(4) 651 367180200 Power CT27^2Arc(3) 676 367549296 Power CT27^2T1T1 702 367918392 Power CT27^2T1 730 368287488 Power CT27^2+1 731 414162876 Add 1 factors 732 435069528 Add 2 factors 733 447750612 Add 3 factors 734 452206128 Add 4 factors 743 456661644 Add 13 factors 757 501216480 Power N-CT29^2Arc(3) 784 514212060 Power N-CT29^2T1T1 812 527207640 Power N-CT29^2T1 841 540203220 Power N-CT29^2 842 586101072 Add 1 factors 843 607032060 Add 2 factors 844 619713144 Add 3 factors 845 624168660 Add 4 factors 854 628624176 Add 13 factors 855 674522028 Add 13 factors 856 695453016 Add 13 factors 857 708134100 Add 13 factors 858 712589616 Add 13 factors 867 717045132 Add 13 factors 868 732145954 Power N-CT31^2T3 870 739071383 Power N-CT31^2T2T1 871 741569532 Power N-CT31^2Arc(3) 899 745141534 Power N-CT31^2T2 900 747639683 Power N-CT31^2T1T1 930 753709834 Power N-CT31^2T1 961 759779985 Power N-CT31^2 962 796423305 Power N-CT31^2+1 989 805294476 Power N-CT41^2Trin3,3,13 1014 809301960 Power N-CT41^2Trin2,3,13 1036 809563896 Power N-CT37^2T9 1039 809697420 Power N-CT41^2Trin1,3,13 1064 810013788 Power N-CT41^2T13T3 1066 813704904 Power N-CT41^2Trin1,2,13 1067 813783996 Power N-CT41^2Arc(3)T13 1092 814021272 Power N-CT41^2T13T2 1093 814100364 Power N-CT41^2Arc(2)T13 1120 814416732 Power N-CT41^2T13T1 1148 814733100 Power N-CT41^2T13 1160 827412312 Power N-CT41^2T12T1 1189 827728680 Power N-CT41^2T12 1200 835980612 Power N-CT41^2T11T1 1230 836296980 Power N-CT41^2T11 1234 837983808 Power N-CT41^2Trin3,3,6 1269 838221084 Power N-CT41^2Trin3,3,5 1339 838458360 Power N-CT41^2Trin3,3,3 1374 842465844 Power N-CT41^2Trin2,3,3 1409 842861304 Power N-CT41^2Trin1,3,3 1444 843177672 Power N-CT41^2T3T3 1446 846868788 Power N-CT41^2Trin1,2,3 1447 846947880 Power N-CT41^2Arc(3)T3 1482 847185156 Power N-CT41^2T3T2 1483 847264248 Power N-CT41^2Arc(2)T3 1520 847580616 Power N-CT41^2T3T1 1558 847896984 Power N-CT41^2T3 1560 851588100 Power N-CT41^2T2T1 1561 851667192 Power N-CT41^2Arc(3) 1599 851904468 Power N-CT41^2T2 1600 851983560 Power N-CT41^2T1T1 1640 852299928 Power N-CT41^2T1 1681 852616296 Power N-CT41^2 1682 898514148 Add 1 factors 1683 919445136 Add 2 factors 1684 932126220 Add 3 factors 1685 936581736 Add 4 factors 1694 941037252 Add 13 factors 1695 986935104 Add 13 factors 1720 1001812343 Power N-CT43^2T3 1763 1002128711 Power N-CT43^2T2 1849 1013629666 Power N-CT43^2 1891 1054625723 Power N-CT61^2T30 1952 1057068611 Power N-CT61^2T29 2013 1059048288 Power N-CT61^2T28 2074 1059364656 Power N-CT61^2T27 2135 1059681024 Power N-CT61^2T26 2196 1059918300 Power N-CT61^2T25 2318 1060155576 Power N-CT61^2T23 2379 1064163060 Power N-CT61^2T22 2440 1064558520 Power N-CT61^2T21 2501 1064874888 Power N-CT61^2T20 2623 1076375843 Power N-CT61^2T18 3724 1081202472 Power N-CT61^2+3 3751 1123651018 Power N-CT67^2Arc(12) 3807 1144874038 Power N-CT67^2Arc(11) 3864 1166097058 Power N-CT67^2Arc(10) 3922 1187320078 Power N-CT67^2Arc(9) 3981 1208543098 Power N-CT67^2Arc(8) 4041 1229766118 Power N-CT67^2Arc(7) 4097 1235659789 perfect hash family256,4097,13,c 4098 1235662832 Power CT64^2+2 4102 1250989138 Power N-CT67^2Arc(6) 4164 1272212158 Power N-CT67^2Arc(5) 4227 1293435178 Power N-CT67^2Arc(4) 4291 1314658198 Power N-CT67^2Arc(3) 4356 1335881218 Power N-CT67^2T1T1 5040 1342282248 Power CT31^3T17S30 5400 1346709203 Power CT31^3T16S30 5758 1351164719 Power CT31^3T15S30 6119 1354232649 Power CT31^3T14S30 6477 1356762671 Power CT31^3T13S30 9351 1360104312 Power CT31^3T5S30 10000 1360473408 Power CT31^3T3S30

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