Table for CAN(5,k,17) for k up to 10000

Last Updated Tue Mar 8 20:11:31 MST 2022

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;5,k,17) 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 18 1419857 orthogonal array 20 2476095 orthogonal array fuse fuse 21 2839713 CPHF Random Extension (CLS) 34 4176033 4-Restricted SCPHF RE (CL) 37 4254641 3-Restricted SCPHF RE (CL) 39 4259265 2-Restricted SCPHF RE (CL) 41 4259569 CPHF IPO 3 (WCS) 56 5512369 4,4-Restricted SCPHF RE (CL) 61 5595873 4-Restricted SCPHF RE (CL) 68 5674481 3-Restricted SCPHF RE (CL) 70 5679105 2-Restricted SCPHF RE (CL) 80 5679425 CPHF IPO 4 (WCS) 97 6932209 4,4-Restricted SCPHF RE (CL) 112 7015713 4-Restricted SCPHF RE (CL) 120 7094321 3-Restricted SCPHF RE (CL) 128 7098945 2-Restricted SCPHF RE (CL) 136 7099281 CPHF IPO 5 (WCS) 157 8268545 4,4,4-Restricted SCPHF RE (CL) 181 8352049 4,4-Restricted SCPHF RE (CL) 199 8435553 4-Restricted SCPHF RE (CL) 217 8514161 3-Restricted SCPHF RE (CL) 219 8518785 2-Restricted SCPHF RE (CL) 223 8519057 SCPHF Random Extension (CLS) 228 8519137 CPHF Random Extension (CLS) 278 9688385 4,4,4-Restricted SCPHF RE (CL) 309 9771889 4,4-Restricted SCPHF RE (CL) 358 9855393 4-Restricted SCPHF RE (CL) 400 9934001 3-Restricted SCPHF RE (CL) 407 9938625 2-Restricted SCPHF RE (CL) 408 9938993 CPHF Random Extension (CLS) 480 11108225 4,4,4-Restricted SCPHF RE (CL) 555 11191729 4,4-Restricted SCPHF RE (CL) 620 11275233 4-Restricted SCPHF RE (CL) 663 11353841 3-Restricted SCPHF RE (CL) 718 11358465 2-Restricted SCPHF RE (CL) 721 11358737 SCPHF Random Extension (CLS) 722 16542241 Add 1 factors 723 19678353 4-Restricted SCPHF RE (CL) fuse fuse 838 19801815 3-Restricted SCPHF RE (CL) fuse fuse 851 19808313 2-Restricted SCPHF RE (CL) fuse fuse 852 25065801 Add 1 factors 853 28912969 Add 2 factors 854 30249305 Add 3 factors 855 31579143 Add 17 factors 868 31585641 Add 17 factors 928 33825696 perfect hash family3,928,620 950 33982912 perfect hash family3,993,663T43 977 33992160 perfect hash family3,1074,717T97 979 33992704 perfect hash family3,1080,721T101 993 34061520 perfect hash family3,993,663 1020 34070768 perfect hash family3,1074,717T54 1022 34071312 perfect hash family3,1080,721T58 1075 34075392 perfect hash family3,1075,718 1077 34075936 perfect hash family3,1080,721T3 1080 34076208 perfect hash family3,1080,721 1102 38168736 Power N-CT41^2Trin2,7,7 1156 38169040 Power N-CT41^2T7T7 1198 38247344 Power N-CT41^2Trin2,4,7 1258 38247648 Power N-CT41^2T7T4 1262 38251968 Power N-CT41^2Trin2,2,7 1326 38252272 Power N-CT41^2T7T2 1394 38252576 Power N-CT41^2T7 1443 38330880 Power N-CT41^2T4T2 1517 38331184 Power N-CT41^2T4 1521 38335504 Power N-CT41^2T2T2 1599 38335808 Power N-CT41^2T2 1681 38336112 Power N-CT41^2 1790 43916912 perfect hash family4,3125,625T267 2000 43995520 perfect hash family4,3125,625T225 2035 44000144 perfect hash family4,3125,625T218 2040 44000512 perfect hash family4,3125,625T217 2400 45169744 perfect hash family4,3125,625T145 2775 45253248 perfect hash family4,3125,625T70 3100 45336752 perfect hash family4,3125,625T5 3125 45415360 perfect hash family4,3125,625 3239 49694960 Power N-CT79^2T38 3416 50279344 Power N-CT61^2T5 3721 50362848 Power N-CT61^2 3752 50908208 Power N-CT67^2T11 3755 50942496 Power N-CT71^2Trin1,3,15 3808 50942816 Power N-CT71^2T15T3 3811 50946800 Power N-CT71^2Arc(3)T15 3865 50947120 Power N-CT71^2Arc(2)T15 3920 50947440 Power N-CT71^2T15T1 4424 50947760 Power N-CT79^2T23 4819 51031264 Power N-CT79^2T18 5372 51109872 Power N-CT79^2T11 5530 51114496 Power N-CT79^2T9 6242 51114816 Power N-CT79^2+1 6243 58813776 Add 1 factors 6400 59884304 Power N-CT83^2T3T3 6596 61132144 Power N-CT97^2T29 6790 61136768 Power N-CT97^2T27 7760 61137088 Power N-CT97^2T17 8720 61805120 perfect hash family9,11881,109T29 9409 62389872 Power N-CT97^2 9558 62470976 perfect hash family9,14986,126T46 10000 63057904 perfect hash family9,11449,107T10

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