Table for CAN(6,k,16) for k up to 10000

Last Updated Sat Nov 16 19:19:53 MST 2019

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,16) 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 17 16777216 orthogonal array 18 24137567 orthogonal array fuse 19 39866207 Add 1 factors 20 47045875 orthogonal array fuse fuse fuse 22 49283056 5-Restricted SCPHF RE (CL) 25 50266096 4-Restricted SCPHF RE (CL) 26 50331616 SCPHF Random Extension (CLS) 33 65011696 5,5-Restricted SCPHF RE (CL) 35 66060256 5-Restricted SCPHF RE (CL) 39 67043296 4-Restricted SCPHF RE (CL) 40 67108816 SCPHF Random Extension (CLS) 41 67108861 CPHF Random Extension (CLS) 51 81788896 5,5-Restricted SCPHF RE (CL) 56 82837456 5-Restricted SCPHF RE (CL) 58 83820496 4-Restricted SCPHF RE (CL) 63 83881936 3-Restricted SCPHF RE (CL) 64 83885776 2-Restricted SCPHF RE (CL) 66 83886016 SCPHF Random Extension (CLS) 73 97517536 5,5,5-Restricted SCPHF RE (CL) 82 98566096 5,5-Restricted SCPHF RE (CL) 89 99614656 5-Restricted SCPHF RE (CL) 98 100597696 4-Restricted SCPHF RE (CL) 103 100659136 3-Restricted SCPHF RE (CL) 104 100662976 2-Restricted SCPHF RE (CL) 113 114294736 5,5,5-Restricted SCPHF RE (CL) 127 115343296 5,5-Restricted SCPHF RE (CL) 141 116391856 5-Restricted SCPHF RE (CL) 150 117374896 4-Restricted SCPHF RE (CL) 156 117436336 3-Restricted SCPHF RE (CL) 159 117440176 2-Restricted SCPHF RE (CL) 163 117440416 SCPHF Random Extension (CLS) 164 117440506 CPHF Random Extension (CLS) 236 134217616 SCPHF Random Extension (CLS) 268 193100431 SCPHF Random Extension (CLS) fuse 289 268435440 Power CT17^2 290 346026480 Add 1 factors 291 383746800 Add 2 factors 292 414221040 Add 3 factors 293 429949680 Add 4 factors 305 445678320 Add 16 factors 306 484882160 Add 17 factors 312 536211424 Martirosyan-TVT 313 536334304 Martirosyan-TVT variant 316 536453344 Martirosyan-TVT 317 536594704 Martirosyan-TVT variant 318 536736064 Martirosyan-TVT 512 536870416 perfect hash family32,512,16,c 513 536870880 perfect hash family32,513,17 514 629265120 Add 1 factors 530 671088075 perfect hash family5,530,236 536 688559824 Martirosyan-TVT 544 763894833 Martirosyan-TVT 545 764132913 Martirosyan-TVT variant 546 764370993 Martirosyan-TVT 547 777607649 Martirosyan-TVT variant 550 793455761 Martirosyan-TVT 551 793612673 Martirosyan-TVT variant 568 793769841 Martirosyan-TVT 577 794752641 Martirosyan-TVT variant 578 803804929 Martirosyan-TVT 625 804257520 Power CT25^2 639 805305690 perfect hash family6,639,236 641 864188505 perfect hash family6,651,237S5 648 889126785 Power N-CT41^2Trin1,2,24 663 889126830 Power N-CT41^2T24T2 664 889192305 Power N-CT41^2Arc(2)T24 680 889192350 Power N-CT41^2T24T1 697 889192395 Power N-CT41^2T24 702 896487181 Power N-CT41^2T23T2 703 896552656 Power N-CT41^2Arc(2)T23 720 896552701 Power N-CT41^2T23T1 738 896552746 Power N-CT41^2T23 741 912215821 Power N-CT41^2T22T2 742 912281296 Power N-CT41^2Arc(2)T22 760 912281341 Power N-CT41^2T22T1 779 912281386 Power N-CT41^2T22 780 919395489 Power N-CT41^2T21T2 781 919460964 Power N-CT41^2Arc(2)T21 800 919461009 Power N-CT41^2T21T1 820 919461054 Power N-CT41^2T21 822 920584065 Power N-CT41^2Trin2,8,15 825 920584110 Power N-CT41^2T16T8 840 920649585 Power N-CT41^2Trin1,8,15 858 920649630 Power N-CT41^2T15T8 870 921632625 Power N-CT41^2Trin2,6,15 875 921632670 Power N-CT41^2T16T6 890 921698145 Power N-CT41^2Trin1,6,15 910 921698190 Power N-CT41^2T15T6 929 922550145 Power N-CT41^2Trin2,2,16 966 922615665 Power N-CT41^2Trin2,2,15 975 922615710 Power N-CT41^2T16T2 990 922681185 Power N-CT41^2Trin1,2,15 1014 922681230 Power N-CT41^2T15T2 1025 922681275 Power N-CT41^2T16 1040 922746750 Power N-CT41^2T15T1 1066 922746795 Power N-CT41^2T15 1089 935329710 Power N-CT41^2T8T8 1101 936312705 Power N-CT41^2Trin2,6,8 1128 936378225 Power N-CT41^2Trin1,6,8 1155 936378270 Power N-CT41^2T8T6 1225 937295745 Power N-CT41^2Trin2,2,8 1256 937361265 Power N-CT41^2Trin1,2,8 1287 937361310 Power N-CT41^2T8T2 1288 937426785 Power N-CT41^2Arc(2)T8 1320 937426830 Power N-CT41^2T8T1 1353 937426875 Power N-CT41^2T8 1365 938409870 Power N-CT41^2T6T2 1366 938475345 Power N-CT41^2Arc(2)T6 1400 938475390 Power N-CT41^2T6T1 1435 938475435 Power N-CT41^2T6 1447 939327345 Power N-CT41^2Trin2,2,2 1484 939392865 Power N-CT41^2Trin1,2,2 1521 939392910 Power N-CT41^2T2T2 1522 939458385 Power N-CT41^2Arc(2)T2 1560 939458430 Power N-CT41^2T2T1 1599 939458475 Power N-CT41^2T2 1600 939523950 Power N-CT41^2T1T1 1640 939523995 Power N-CT41^2T1 1681 939524040 Power N-CT41^2 1682 1065326280 Add 1 factors 1833 1130298930 Power N-CT47^2T8 1880 1130364450 Power N-CT47^2T7 1927 1130364495 Power N-CT47^2T6 1964 1141898610 Power N-CT53^2Trin2,2,13 2013 1141898655 Power N-CT53^2Trin2,2,12 2040 1142947170 Power N-CT53^2T13T2 2091 1142947215 Power N-CT53^2T12T2 2120 1143995730 Power N-CT53^2T13 2173 1143995775 Power N-CT53^2T12 2213 1145044530 perfect hash family14,2213,51 2258 1156468095 Power N-CT59^2Trin1,3,18 2296 1156529535 Power N-CT59^2T18T3 2503 1156578690 Power N-CT53^2Trin2,2,2 2601 1157627250 Power N-CT53^2T2T2 2703 1158675810 Power N-CT53^2T2 2812 1159724370 Power N-CT53^2+3 2856 1171209570 Power N-CT59^2T8T3 2977 1171213650 Power N-CT59^2Trin3,3,3 3083 1172196690 Power N-CT59^2Trin1,3,3 3111 1172254050 Power N-CT61^2T10 3136 1172258130 Power N-CT59^2T3T3 3139 1173118290 Power N-CT59^2Arc(3)T3 3193 1173179730 Power N-CT59^2Arc(2)T3 3248 1173241170 Power N-CT59^2T3T1 3416 1173302610 Power N-CT61^2T5 3538 1174285650 Power N-CT61^2T3 3723 1174347090 Power N-CT61^2+2 3724 1174400850 Power N-CT61^2+3 3726 1174404210 perfect hash family14,3726,66 3751 1201667250 Power N-CT67^2Arc(12) 3807 1215298770 Power N-CT67^2Arc(11) 3825 1226833155 Power N-CT73^2Trin7,7,9 3943 1226833395 Power N-CT73^2Trin7,7,7 3969 1240456755 Power N-CT73^2T10T10 4032 1240460595 Power N-CT73^2T10T9 4158 1240460835 Power N-CT73^2T10T7 4224 1240464675 Power N-CT73^2T9T7 4356 1240464915 Power N-CT73^2T7T7 4599 1254092355 Power N-CT73^2T10 4672 1254096195 Power N-CT73^2T9 4818 1254096435 Power N-CT73^2T7 4977 1266675075 Power N-CT79^2T16 5056 1266678915 Power N-CT79^2T15 5214 1266679155 Power N-CT79^2T13 5329 1267727955 Power N-CT73^2 5347 1277164755 Power N-CT83^2Arc(2)T17 5412 1278213315 Power N-CT83^2T17T1 5607 1279257795 Power N-CT89^2T26 5696 1279261635 Power N-CT89^2T25 5874 1279261875 Power N-CT89^2T23 6244 1281359235 Power N-CT79^2+3 6253 1286602035 Power N-CT83^2Arc(8) 6329 1287650595 Power N-CT83^2Arc(7) 6406 1288699155 Power N-CT83^2Arc(6) 6484 1289747715 Power N-CT83^2Arc(5) 6563 1290796275 Power N-CT83^2Arc(4) 6592 1291795395 perfect hash family13,10609,103T39 6798 1291795635 perfect hash family13,10609,103T37 7298 1293941955 Power N-CT89^2T7 7921 1294990515 Power N-CT89^2 7954 1305738435 Power N-CT97^2T15 8036 1306414275 Power N-CT101^2T19T3 8446 1306475715 perfect hash family13,10609,103T21 8633 1306786995 Power N-CT97^2T8 8722 1307462835 Power N-CT101^2T12T3 9167 1307524275 perfect hash family13,10609,103T14 9410 1307770035 Power N-CT97^2+1 9604 1308445875 Power N-CT101^2T3T3 10000 1308507315 perfect hash family13,10609,103T5

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