Table for CAN(6,k,14) 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,14) 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 7529536 composition 8 8724225 Augment OA 9 9383502 Augment OA 10 10083278 Augment OA 11 10822128 Augment OA 12 11598564 Augment OA 13 12407628 Augment OA 14 13241592 Augment OA 17 16777212 orthogonal array fuse fuse 18 24137563 orthogonal array fuse fuse fuse 19 36041819 Add 1 factors 20 46266943 Add 2 factors 22 49283052 5-Restricted SCPHF RE (CL) fuse fuse 25 50266092 4-Restricted SCPHF RE (CL) fuse fuse 26 50331612 SCPHF Random Extension (CLS) fuse fuse 33 65011692 5,5-Restricted SCPHF RE (CL) fuse fuse 35 66060252 5-Restricted SCPHF RE (CL) fuse fuse 39 67043292 4-Restricted SCPHF RE (CL) fuse fuse 40 67108812 SCPHF Random Extension (CLS) fuse fuse 41 67108857 CPHF Random Extension (CLS) fuse fuse 51 81788892 5,5-Restricted SCPHF RE (CL) fuse fuse 56 82837452 5-Restricted SCPHF RE (CL) fuse fuse 58 83820492 4-Restricted SCPHF RE (CL) fuse fuse 63 83881932 3-Restricted SCPHF RE (CL) fuse fuse 64 83885772 2-Restricted SCPHF RE (CL) fuse fuse 66 83886012 SCPHF Random Extension (CLS) fuse fuse 73 97517532 5,5,5-Restricted SCPHF RE (CL) fuse fuse 82 98566092 5,5-Restricted SCPHF RE (CL) fuse fuse 89 99614652 5-Restricted SCPHF RE (CL) fuse fuse 98 100597692 4-Restricted SCPHF RE (CL) fuse fuse 103 100659132 3-Restricted SCPHF RE (CL) fuse fuse 104 100662972 2-Restricted SCPHF RE (CL) fuse fuse 113 114294732 5,5,5-Restricted SCPHF RE (CL) fuse fuse 127 115343292 5,5-Restricted SCPHF RE (CL) fuse fuse 141 116391852 5-Restricted SCPHF RE (CL) fuse fuse 150 117374892 4-Restricted SCPHF RE (CL) fuse fuse 156 117436332 3-Restricted SCPHF RE (CL) fuse fuse 159 117440172 2-Restricted SCPHF RE (CL) fuse fuse 163 117440412 SCPHF Random Extension (CLS) fuse fuse 164 117440502 CPHF Random Extension (CLS) fuse fuse 236 134217612 SCPHF Random Extension (CLS) fuse fuse 237 189401468 Add 1 factors 268 193100427 SCPHF Random Extension (CLS) fuse fuse fuse 269 251457999 Add 1 factors 289 268435376 Power CT17^2 290 327274520 Add 1 factors 291 352293332 Add 2 factors 292 383165614 Add 3 factors 294 390577239 Add 5 factors 295 398899311 Add 6 factors 305 441115376 Add 16 factors 306 478888304 Add 17 factors 312 484579536 Martirosyan-TVT 313 484684416 Martirosyan-TVT variant 316 485309160 Martirosyan-TVT 317 485429430 Martirosyan-TVT variant 318 485549700 Martirosyan-TVT 319 496613936 Martirosyan-TVT variant 320 507677932 Martirosyan-TVT 321 507684262 Martirosyan-TVT variant 326 507690592 Martirosyan-TVT 328 507690682 Martirosyan-TVT 330 524467792 Martirosyan-TVT 339 525319552 Martirosyan-TVT variant 340 527626512 Martirosyan-TVT 341 528627612 Martirosyan-TVT variant 352 530210152 Martirosyan-TVT 353 530216557 Martirosyan-TVT variant 370 530222962 Martirosyan-TVT 374 531021682 Martirosyan-TVT 384 531692104 perfect hash family32,512,16T4 416 532501168 perfect hash family32,512,16T3 448 533335132 perfect hash family32,512,16T2 512 536870412 perfect hash family32,512,16,c fuse fuse 513 536870752 perfect hash family32,513,17 514 606935656 Add 1 factors 515 638469704 Add 2 factors 536 644348268 Martirosyan-TVT 538 702705840 Martirosyan-TVT 544 719683217 Martirosyan-TVT 545 720881855 Martirosyan-TVT variant 546 722727077 Martirosyan-TVT 547 735957269 Martirosyan-TVT variant 550 751798917 Martirosyan-TVT 551 751955765 Martirosyan-TVT variant 568 752112869 Martirosyan-TVT 578 752964629 Martirosyan-TVT 625 804257456 Power CT25^2 639 805305666 perfect hash family6,639,236 641 860489522 perfect hash family6,651,237S5 648 889126729 Power N-CT41^2Trin1,2,24 663 889126774 Power N-CT41^2T24T2 664 889192249 Power N-CT41^2Arc(2)T24 680 889192294 Power N-CT41^2T24T1 697 889192339 Power N-CT41^2T24 702 896487125 Power N-CT41^2T23T2 703 896552600 Power N-CT41^2Arc(2)T23 720 896552645 Power N-CT41^2T23T1 738 896552690 Power N-CT41^2T23 741 908391381 Power N-CT41^2T22T2 742 908456856 Power N-CT41^2Arc(2)T22 760 908456901 Power N-CT41^2T22T1 779 908456946 Power N-CT41^2T22 780 918616505 Power N-CT41^2T21T2 781 918681980 Power N-CT41^2Arc(2)T21 800 918682025 Power N-CT41^2T21T1 820 918682070 Power N-CT41^2T21 822 920584009 Power N-CT41^2Trin2,8,15 825 920584054 Power N-CT41^2T16T8 840 920649529 Power N-CT41^2Trin1,8,15 858 920649574 Power N-CT41^2T15T8 870 921632569 Power N-CT41^2Trin2,6,15 875 921632614 Power N-CT41^2T16T6 890 921698089 Power N-CT41^2Trin1,6,15 910 921698134 Power N-CT41^2T15T6 929 922550089 Power N-CT41^2Trin2,2,16 966 922615609 Power N-CT41^2Trin2,2,15 975 922615654 Power N-CT41^2T16T2 990 922681129 Power N-CT41^2Trin1,2,15 1014 922681174 Power N-CT41^2T15T2 1025 922681219 Power N-CT41^2T16 1040 922746694 Power N-CT41^2T15T1 1066 922746739 Power N-CT41^2T15 1089 935329654 Power N-CT41^2T8T8 1101 936312649 Power N-CT41^2Trin2,6,8 1128 936378169 Power N-CT41^2Trin1,6,8 1155 936378214 Power N-CT41^2T8T6 1225 937295689 Power N-CT41^2Trin2,2,8 1256 937361209 Power N-CT41^2Trin1,2,8 1287 937361254 Power N-CT41^2T8T2 1288 937426729 Power N-CT41^2Arc(2)T8 1320 937426774 Power N-CT41^2T8T1 1353 937426819 Power N-CT41^2T8 1365 938409814 Power N-CT41^2T6T2 1366 938475289 Power N-CT41^2Arc(2)T6 1400 938475334 Power N-CT41^2T6T1 1435 938475379 Power N-CT41^2T6 1447 939327289 Power N-CT41^2Trin2,2,2 1484 939392809 Power N-CT41^2Trin1,2,2 1521 939392854 Power N-CT41^2T2T2 1522 939458329 Power N-CT41^2Arc(2)T2 1560 939458374 Power N-CT41^2T2T1 1599 939458419 Power N-CT41^2T2 1600 939523894 Power N-CT41^2T1T1 1640 939523939 Power N-CT41^2T1 1681 939523984 Power N-CT41^2 1682 1034923288 Add 1 factors 1683 1080733780 Add 2 factors 1684 1127749742 Add 3 factors 1686 1129246327 Add 5 factors 1833 1130298874 Power N-CT47^2T8 1880 1130364394 Power N-CT47^2T7 1927 1130364439 Power N-CT47^2T6 1964 1141898554 Power N-CT53^2Trin2,2,13 2013 1141898599 Power N-CT53^2Trin2,2,12 2040 1142947114 Power N-CT53^2T13T2 2091 1142947159 Power N-CT53^2T12T2 2120 1143995674 Power N-CT53^2T13 2173 1143995719 Power N-CT53^2T12 2213 1145044474 perfect hash family14,2213,51 2258 1156468039 Power N-CT59^2Trin1,3,18 2296 1156529479 Power N-CT59^2T18T3 2503 1156578634 Power N-CT53^2Trin2,2,2 2601 1157627194 Power N-CT53^2T2T2 2703 1158675754 Power N-CT53^2T2 2812 1159724314 Power N-CT53^2+3 2856 1171209514 Power N-CT59^2T8T3 2977 1171213594 Power N-CT59^2Trin3,3,3 3083 1172196634 Power N-CT59^2Trin1,3,3 3111 1172253994 Power N-CT61^2T10 3136 1172258074 Power N-CT59^2T3T3 3139 1173118234 Power N-CT59^2Arc(3)T3 3193 1173179674 Power N-CT59^2Arc(2)T3 3248 1173241114 Power N-CT59^2T3T1 3416 1173302554 Power N-CT61^2T5 3538 1174285594 Power N-CT61^2T3 3723 1174347034 Power N-CT61^2+2 3724 1174400794 Power N-CT61^2+3 3726 1174404154 perfect hash family14,3726,66 3751 1201667194 Power N-CT67^2Arc(12) 3807 1215298714 Power N-CT67^2Arc(11) 3825 1226833103 Power N-CT73^2Trin7,7,9 3943 1226833343 Power N-CT73^2Trin7,7,7 3969 1240456703 Power N-CT73^2T10T10 4032 1240460543 Power N-CT73^2T10T9 4158 1240460783 Power N-CT73^2T10T7 4224 1240464623 Power N-CT73^2T9T7 4356 1240464863 Power N-CT73^2T7T7 4599 1254092303 Power N-CT73^2T10 4672 1254096143 Power N-CT73^2T9 4818 1254096383 Power N-CT73^2T7 4977 1266675023 Power N-CT79^2T16 5056 1266678863 Power N-CT79^2T15 5214 1266679103 Power N-CT79^2T13 5329 1267727903 Power N-CT73^2 5347 1277164703 Power N-CT83^2Arc(2)T17 5412 1278213263 Power N-CT83^2T17T1 5607 1279257743 Power N-CT89^2T26 5696 1279261583 Power N-CT89^2T25 5874 1279261823 Power N-CT89^2T23 6244 1281359183 Power N-CT79^2+3 6253 1286601983 Power N-CT83^2Arc(8) 6329 1287650543 Power N-CT83^2Arc(7) 6406 1288699103 Power N-CT83^2Arc(6) 6484 1289747663 Power N-CT83^2Arc(5) 6563 1290796223 Power N-CT83^2Arc(4) 6592 1291795343 perfect hash family13,10609,103T39 6798 1291795583 perfect hash family13,10609,103T37 7298 1293941903 Power N-CT89^2T7 7921 1294990463 Power N-CT89^2 7954 1305738383 Power N-CT97^2T15 8036 1306414223 Power N-CT101^2T19T3 8446 1306475663 perfect hash family13,10609,103T21 8633 1306786943 Power N-CT97^2T8 8722 1307462783 Power N-CT101^2T12T3 9167 1307524223 perfect hash family13,10609,103T14 9410 1307769983 Power N-CT97^2+1 9604 1308445823 Power N-CT101^2T3T3 10000 1308507263 perfect hash family13,10609,103T5

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