Table for CAN(5,k,18) 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,18) 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 6 1889568 Derive from strength 6 7 1955178 Ji-Li-Yin 8 2235668 Augment OA 9 2360788 Augment OA 20 2476097 orthogonal array fuse 21 4444632 extended OA (Colbourn) special fuse 22 4945337 3-Restricted SCPHF RE (CL) fuse 23 4952195 CPHF IPO 2 (WCS) fuse 24 6436333 orthogonal array fuse fuse fuse fuse fuse 37 7297955 4-Restricted SCPHF RE (CL) fuse 40 7421417 3-Restricted SCPHF RE (CL) fuse 41 7428257 SCPHF Random Extension (CLS) fuse 45 7428293 CPHF IPO 3 (WCS) fuse 60 9643733 4,4-Restricted SCPHF RE (CL) fuse 68 9774035 4-Restricted SCPHF RE (CL) fuse 75 9897497 3-Restricted SCPHF RE (CL) fuse 77 9903995 2-Restricted SCPHF RE (CL) fuse 78 9904337 SCPHF Random Extension (CLS) fuse 89 9904391 CPHF IPO 4 (WCS) fuse 107 12119813 4,4-Restricted SCPHF RE (CL) fuse 126 12250115 4-Restricted SCPHF RE (CL) fuse 136 12373577 3-Restricted SCPHF RE (CL) fuse 143 12380075 2-Restricted SCPHF RE (CL) fuse 180 14465591 4,4,4-Restricted SCPHF RE (CL) fuse 207 14595893 4,4-Restricted SCPHF RE (CL) fuse 233 14726195 4-Restricted SCPHF RE (CL) fuse 258 14849657 3-Restricted SCPHF RE (CL) fuse 262 14856155 2-Restricted SCPHF RE (CL) fuse 269 14856587 CPHF Random Extension (CLS) fuse 343 16941671 4,4,4-Restricted SCPHF RE (CL) fuse 373 17071973 4,4-Restricted SCPHF RE (CL) fuse 446 17202275 4-Restricted SCPHF RE (CL) fuse 461 17325737 3-Restricted SCPHF RE (CL) fuse 466 17332235 2-Restricted SCPHF RE (CL) fuse 470 17332577 SCPHF Random Extension (CLS) fuse 473 17332685 CPHF Random Extension (CLS) fuse 597 19417751 4,4,4-Restricted SCPHF RE (CL) fuse 671 19548053 4,4-Restricted SCPHF RE (CL) fuse 723 19678355 4-Restricted SCPHF RE (CL) fuse 838 19801817 3-Restricted SCPHF RE (CL) fuse 851 19808315 2-Restricted SCPHF RE (CL) fuse 852 26957699 Add 1 factors 853 32118695 Add 2 factors 854 35653553 Add 3 factors 855 36240984 Add 4 factors 856 36454581 Add 5 factors 857 38429531 Add 19 factors 860 38436029 Add 19 factors 870 38455523 Add 19 factors 871 45604907 Add 19 factors 872 50765903 Add 19 factors 873 54300761 Add 19 factors 874 54888192 Add 19 factors 875 55101789 Add 19 factors 878 56929368 perfect hash family3,1254,837T376 883 56935866 perfect hash family3,1254,837T371 887 56936208 perfect hash family3,1254,837T367 890 56936316 perfect hash family3,1254,837T364 894 56949204 perfect hash family3,1275,851T381 897 56949312 perfect hash family3,1275,851T378 931 58513854 perfect hash family3,1005,671T74 1005 58644156 perfect hash family3,1005,671 1031 58904760 perfect hash family3,1083,723T52 1083 59035062 perfect hash family3,1083,723 1088 59151684 perfect hash family3,1254,837T166 1095 59164680 perfect hash family3,1275,851T180 1140 59281986 perfect hash family3,1254,837T114 1147 59294982 perfect hash family3,1275,851T128 1255 59405448 perfect hash family3,1255,838 1262 59418444 perfect hash family3,1275,851T13 1275 59424942 perfect hash family3,1275,851 1276 66574326 Add 1 factors 1336 66586860 Power N-CT41^2Trin1,4,4 1369 66593700 Power N-CT41^2T4T4 1375 66696642 Power N-CT41^2Arc(4)T4 1409 66703482 Power N-CT41^2Arc(3)T4 1444 66710322 Power N-CT41^2Arc(2)T4 1480 66717162 Power N-CT41^2T4T1 1517 66724002 Power N-CT41^2T4 1591 66724290 Power N-CT43^2T6 1600 66840624 Power N-CT41^2T1T1 1640 66847464 Power N-CT41^2T1 1720 66847752 Power N-CT43^2T3 1763 66854592 Power N-CT43^2T2 1851 66854628 Power N-CT43^2+2 1865 75716128 perfect hash family4,3125,625T252 2230 75846430 perfect hash family4,3125,625T179 2305 75969892 perfect hash family4,3125,625T164 2330 75976390 perfect hash family4,3125,625T159 2350 75976732 perfect hash family4,3125,625T155 2365 75976840 perfect hash family4,3125,625T152 2985 78061906 perfect hash family4,3125,625T28 3125 78192208 perfect hash family4,3125,625 3293 86533074 Power N-CT89^2T52 3334 86656464 Power N-CT79^2Trin1,4,34 3375 86656518 Power N-CT79^2T34T4 3560 86656536 Power N-CT89^2T49 3649 86663376 Power N-CT89^2T48 4005 86663412 Power N-CT89^2T44 4020 87836004 Power N-CT67^2T7 4490 87966306 Power N-CT67^2+1 4624 88830540 Power N-CT71^2T3T3 4680 88878798 Power N-CT79^2T19T1 5340 88878852 Power N-CT89^2T29 6052 89009154 Power N-CT89^2T21 6675 89132616 Power N-CT89^2T14 6853 89139114 Power N-CT89^2T12 6942 89139456 Power N-CT89^2T11 7921 89139510 Power N-CT89^2 8000 96567780 Power CT23^3T3T3T3 8400 98536315 Power CT23^3T3T3T2 8800 99037020 Power CT23^3T3T3T1 9200 99043878 Power CT23^3T3T3 9240 101005555 Power CT23^3T3T2T1 9660 101012413 Power CT23^3T3T2 9680 101506260 Power CT23^3T3T1T1 10000 101513118 Power CT23^3T3T1

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