# Table for CAN(5,k,15) for k up to 10000

#### 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,15) 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 759375 Derive from strength 6 7 860625 Ji-Li-Yin 17 1048574 orthogonal array fuse 18 1419853 orthogonal array fuse fuse 19 2278123 AZ1 20 2476091 orthogonal array fuse fuse fuse fuse 24 3145719 perfect hash family3,24,17 26 4002522 Martirosyan-Tran van Trung 28 4008186 Martirosyan-Tran van Trung 30 4017330 Martirosyan-Tran van Trung 32 4018338 Martirosyan-Tran van Trung 34 4025898 Martirosyan-Tran van Trung 36 4673461 Martirosyan-Tran van Trung 37 6281431 AZ1 39 6291438 perfect hash family6,39,17 48 7340011 perfect hash family7,48,17 55 8388584 perfect hash family8,55,17 71 9437157 perfect hash family9,71,17 88 10485730 perfect hash family10,88,17 102 11245104 Power CT17^2T11 119 11346354 Power CT17^2T10 289 11534303 Power CT17^2 290 13596713 AZ1 291 15105563 Add 2 factors 292 15814313 Add 3 factors 293 17346143 Add 4 factors 295 17631503 Add 16 factors 305 17635343 Add 16 factors 306 18935967 Add 17 factors 307 20206410 Power N-CT19^2Arc(3) 324 21064680 Power N-CT19^2T1T1 342 21922950 Power N-CT19^2T1 361 22781220 Power N-CT19^2 378 23725729 Martirosyan-Tran van Trung 448 23742107 Martirosyan-Tran van Trung 512 23758485 Martirosyan-Tran van Trung 544 23866005 Martirosyan-Tran van Trung 546 23942331 Martirosyan-Tran van Trung 556 25502523 Martirosyan-Tran van Trung 578 25522165 Martirosyan-Tran van Trung 580 27895683 Martirosyan-Tran van Trung 582 29424175 Martirosyan-Tran van Trung 584 30132925 Martirosyan-Tran van Trung 586 31664755 Martirosyan-Tran van Trung 590 31950115 Martirosyan-Tran van Trung 610 31953955 Martirosyan-Tran van Trung 612 33254579 Martirosyan-Tran van Trung 614 35628139 Martirosyan-Tran van Trung 620 38641123 Power N-CT31^2T11 627 39274247 Power N-CT29^2Arc(3)T5 649 39283391 Power N-CT29^2Arc(2)T5 672 39292535 Power N-CT29^2T5T1 696 39301679 Power N-CT29^2T5 697 39308735 Power N-CT31^2Arc(2)T7 720 39309743 Power N-CT31^2T7T1 744 39310751 Power N-CT31^2T7 757 40145858 Power N-CT29^2Arc(3) 784 40155002 Power N-CT29^2T1T1 812 40164146 Power N-CT29^2T1 813 40171202 Power N-CT31^2Arc(2)T3 840 40172210 Power N-CT31^2T3T1 868 40173218 Power N-CT31^2T3 871 40180346 Power N-CT31^2Arc(3) 900 40181354 Power N-CT31^2T1T1 930 40182362 Power N-CT31^2T1 962 40183370 Power N-CT31^2+1 964 40258970 Power N-CT31^2+3 965 44042750 AZ1 1024 44201707 Power CT32^2 1026 44284867 Power CT32^2+2 1044 46734600 Power N-CT37^2Arc(10) 1072 48342570 Power N-CT37^2Arc(9) 1088 49336895 Martirosyan-Tran van Trung 1092 49550081 Martirosyan-Tran van Trung 1101 49950540 Power N-CT37^2Arc(8) 1131 51558510 Power N-CT37^2Arc(7) 1162 53166480 Power N-CT37^2Arc(6) 1194 54774450 Power N-CT37^2Arc(5) 1227 56382420 Power N-CT37^2Arc(4) 1235 57671515 perfect hash family55,1235,17 1261 57990390 Power N-CT37^2Arc(3) 1734 59479444 Power CT23^3T17T6T6 2023 59580694 Power CT23^3T16T6T6 4913 59768643 Power CT23^3T6T6T6 5202 60139922 Power CT23^3T6T6T5 5508 60511201 Power CT23^3T6T5T5 5832 60882480 Power CT23^3T5T5T5 6120 61567439 Power CT23^3T6T5T3 6156 61740750 Power CT23^3T5T5T4 6647 61865788 Power CT23^3T6T6 7038 62237067 Power CT23^3T6T5 7452 62608346 Power CT23^3T5T5 7820 63293305 Power CT23^3T6T3 7866 63466616 Power CT23^3T5T4 8280 63664584 Power CT23^3T5T3 8993 63962933 Power CT23^3T6 9522 64334212 Power CT23^3T5 10000 65192482 Power CT23^3T4
Graph: