Table for CAN(6,k,15) 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,15) 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 11390625 composition 8 15080613 Augment OA 17 16777214 orthogonal array fuse 18 24137565 orthogonal array fuse fuse 19 37899705 Add 1 factors 20 47045873 orthogonal array fuse fuse fuse fuse 21 62680755 Add 3 factors 23 67108852 perfect hash family4,23,17 32 79691774 double OA (Colbourn-Zhou) fuse 34 80736254 double OA (Colbourn-Zhou) fuse 35 98279172 Martirosyan-TVT variant 36 103311216 Martirosyan-TVT 37 143637936 Add 1 factors 38 167757486 Add 2 factors 39 167772130 perfect hash family10,39,17 40 184549214 perfect hash family11,40,16,c fuse 44 184549343 perfect hash family11,44,17 50 201326556 perfect hash family12,50,17 53 218103769 perfect hash family13,53,17 60 234880982 perfect hash family14,60,17 80 251658014 perfect hash family15,80,16,c fuse 85 251658195 Power CT17^2Tlev 119 263048819 Power CT17^2T10 136 266738807 Power CT17^2T9 256 268435214 perfect hash family16,256,16,c fuse 289 268435408 Power CT17^2 290 337125568 Add 1 factors 291 368061718 Add 2 factors 292 390694468 Add 3 factors 294 419704671 Add 5 factors 295 435016593 Add 6 factors 305 444555088 Add 16 factors 306 483233808 Add 17 factors 512 536870414 perfect hash family32,512,16,c fuse 513 536870816 perfect hash family32,513,17 514 639318056 Add 1 factors 515 686149106 Add 2 factors 516 715444106 Add 3 factors 517 747011695 Add 5 factors 518 747012097 Add 5 factors 519 768900249 Add 6 factors 521 779133614 Add 16 factors 525 779379374 Add 16 factors 528 779609294 Add 16 factors 529 779609696 Add 16 factors 544 804939927 Martirosyan-TVT 545 806982441 Martirosyan-TVT variant 546 809679147 Martirosyan-TVT 547 823043595 Martirosyan-TVT variant 557 839071467 Martirosyan-TVT variant 578 839725659 Martirosyan-TVT 579 947932460 Martirosyan-TVT variant 580 958575361 Martirosyan-TVT 581 1010635411 Martirosyan-TVT variant 582 1011334041 Martirosyan-TVT 584 1043889291 Martirosyan-TVT 586 1084982516 Martirosyan-TVT 588 1086305516 Martirosyan-TVT 593 1099163259 Add 16 factors 594 1099961979 Add 16 factors 610 1123244331 Martirosyan-TVT 620 1162730694 Power N-CT31^2T11 651 1178365576 Power N-CT31^2T10 713 1182793673 Power N-CT31^2T8 962 1195376595 Power N-CT31^2+1 964 1211043795 Power N-CT31^2+3 1024 1275068368 Power CT32^2 1026 1291780048 Power CT32^2+2 1027 1426108438 Add 1 factors 1028 1482865138 Add 2 factors 1029 1514758888 Add 3 factors 1031 1547589523 Add 5 factors 1040 1569721888 Add 16 factors 1042 1586433568 Add 16 factors 1043 1644905680 Add 17 factors 1044 1751301825 Power N-CT37^2Arc(10) 1045 1790717692 Add 19 factors 1072 1791628545 Power N-CT37^2Arc(9) 1101 1831955265 Power N-CT37^2Arc(8) 1131 1872281985 Power N-CT37^2Arc(7) 1162 1912608705 Power N-CT37^2Arc(6) 1194 1952935425 Power N-CT37^2Arc(5) 1227 1993262145 Power N-CT37^2Arc(4) 1261 2033588865 Power N-CT37^2Arc(3) 1296 2073915585 Power N-CT37^2T1T1 1332 2114242305 Power N-CT37^2T1 1425 2147483264 perfect hash family128,1425,17 2023 2276314694 Power CT31^3T24T14T14 2312 2280004682 Power CT31^3T23T14T14 4913 2281701283 Power CT31^3T14T14T14 5202 2289061634 Power CT31^3T14T14T13 5508 2296421985 Power CT31^3T14T13T13 5832 2303782336 Power CT31^3T13T13T13 6156 2317544476 Power CT31^3T13T13T12 6480 2326690644 Power CT31^3T13T13T11 6498 2331306616 Power CT31^3T13T12T12 6647 2332032921 Power CT31^3T14T14T8 7038 2339393272 Power CT31^3T14T13T8 9248 2344615843 Power CT32^3T15T15 9792 2351976194 Power CT32^3T15T14 10000 2359336545 Power CT31^3T13T13

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