Table for CAN(5,k,16) 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,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 1048576 orthogonal array 18 1419855 orthogonal array fuse 20 2093056 3-Restricted SCPHF RE (CL) 21 2097151 CPHF IPO 2 (WCS) 33 3080176 4-Restricted SCPHF RE (CL) 36 3141616 3-Restricted SCPHF RE (CL) 38 3145456 2-Restricted SCPHF RE (CL) 39 3145726 CPHF IPO 3 (WCS) 53 4063216 4,4-Restricted SCPHF RE (CL) 56 4128736 4-Restricted SCPHF RE (CL) 62 4186096 3,3-Restricted SCPHF RE (CL) 64 4190176 3-Restricted SCPHF RE (CL) 66 4194256 SCPHF Random Extension (CLS) 73 4194301 CPHF IPO 4 (WCS) 92 5111776 4,4-Restricted SCPHF RE (CL) 103 5177296 4-Restricted SCPHF RE (CL) 111 5238736 3-Restricted SCPHF RE (CL) 119 5242576 2-Restricted SCPHF RE (CL) 145 5242876 CPHF IPO 5 (WCS) 146 6094816 4,4,4-Restricted SCPHF RE (CL) 165 6160336 4,4-Restricted SCPHF RE (CL) 185 6225856 4-Restricted SCPHF RE (CL) 197 6287296 3-Restricted SCPHF RE (CL) 206 6291136 2-Restricted SCPHF RE (CL) 207 6291376 SCPHF Random Extension (CLS) 210 6291451 CPHF Random Extension (CLS) 248 7143376 4,4,4-Restricted SCPHF RE (CL) 284 7208896 4,4-Restricted SCPHF RE (CL) 336 7274416 4-Restricted SCPHF RE (CL) 360 7335856 3-Restricted SCPHF RE (CL) 376 7339696 2-Restricted SCPHF RE (CL) 379 7339936 SCPHF Random Extension (CLS) 454 8191936 4,4,4-Restricted SCPHF RE (CL) 515 8257456 4,4-Restricted SCPHF RE (CL) 582 8322976 4-Restricted SCPHF RE (CL) 641 8384416 3-Restricted SCPHF RE (CL) 650 8388256 2-Restricted SCPHF RE (CL) 656 8388496 SCPHF Random Extension (CLS) 766 9240496 4,4,4-Restricted SCPHF RE (CL) 767 13103536 Add 1 factors 768 15906736 Add 2 factors 769 16889776 Add 3 factors 782 17872816 Add 16 factors 783 19588192 Add 17 factors 838 19801813 3-Restricted SCPHF RE (CL) fuse fuse fuse 851 19808311 2-Restricted SCPHF RE (CL) fuse fuse fuse 852 23671351 Add 1 factors 871 24968925 perfect hash family3,871,582 901 25091805 perfect hash family3,960,641T59 905 25099485 perfect hash family3,972,649T67 908 25099965 perfect hash family3,981,655T73 960 25153245 perfect hash family3,960,641 964 25160925 perfect hash family3,972,649T8 967 25161405 perfect hash family3,981,655T14 973 25164765 perfect hash family3,973,650 976 25165245 perfect hash family3,981,655T5 982 25165485 perfect hash family3,982,656 1022 26865405 perfect hash family3,1146,765T124 1031 26869245 perfect hash family3,1146,765T115 1037 26869485 perfect hash family3,1146,765T109 1147 27721485 perfect hash family3,1147,766 1156 31381590 Power N-CT37^2Arc(2)T4 1188 31385430 Power N-CT37^2T4T1 1221 31389270 Power N-CT37^2T4 1227 31439190 Power N-CT37^2Arc(4) 1261 31443030 Power N-CT37^2Arc(3) 1296 31446870 Power N-CT37^2T1T1 1332 31450710 Power N-CT37^2T1 1370 31454550 Power N-CT37^2+1 1371 31457250 Power N-CT37^2+2 1420 32362140 perfect hash family4,3125,625T341 1680 32427660 perfect hash family4,3125,625T289 1800 32489100 perfect hash family4,3125,625T265 1880 32492940 perfect hash family4,3125,625T249 1895 32493180 perfect hash family4,3125,625T246 2270 33345180 perfect hash family4,3125,625T171 2575 33410700 perfect hash family4,3125,625T110 2910 33476220 perfect hash family4,3125,625T43 3125 33537660 perfect hash family4,3125,625 3233 37551975 Power N-CT61^2T8 3242 37609365 Power N-CT67^2Trin3,3,14 3286 37609410 Power N-CT67^2T14T5 3342 37613445 Power N-CT67^2Trin1,3,14 3392 37613490 Power N-CT67^2T14T3 3395 37617480 Power N-CT67^2Arc(3)T14 3416 37617495 Power N-CT61^2T5 3446 37617525 Power N-CT67^2Arc(2)T14 3498 37617570 Power N-CT67^2T14T1 3869 37617615 Power N-CT73^2T20 4088 37683135 Power N-CT73^2T17 4096 37740450 Power N-CT67^2T3T3 4526 37740495 Power N-CT73^2T11 4672 37744575 Power N-CT73^2T9 4818 37748655 Power N-CT73^2T7 5329 37748700 Power N-CT73^2 5330 43177740 Add 1 factors 5518 45080295 Power N-CT89^2T27 5696 45084375 Power N-CT89^2T25 5874 45088455 Power N-CT89^2T23 6497 45088500 Power N-CT89^2T16 6716 45547140 Power N-CT97^2T24T5 6798 45612615 perfect hash family9,10609,103T37 7519 45612660 perfect hash family9,10609,103T30 7924 46005975 Power N-CT89^2+3 7957 46104180 perfect hash family9,11881,109T36 8249 46134900 perfect hash family9,12769,113T40 8732 46137300 perfect hash family9,14986,126T53 9476 46530135 perfect hash family9,10609,103T11 10000 46595655 Power N-CT101^2

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