Table for CAN(6,k,14) for k up to 10000

Last Updated Fri Sep 20 11:45:18 MST 2013

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 8732479 Add a symbol 9 9404208 Add a symbol 10 10127608 Add a symbol 11 10906654 Add a symbol 12 11745627 Add a symbol 13 12649136 Add a symbol 14 13622146 Add a symbol 17 16777212 orthogonal array fuse fuse 18 24137563 orthogonal array fuse fuse fuse 19 36042001 Add 1 factors 20 46269673 Add 2 factors 21 59067801 Add 3 factors 22 60698726 Martirosyan-Tran van Trung 24 65435910 Martirosyan-Tran van Trung 26 68147956 Martirosyan-Tran van Trung 28 71179276 Martirosyan-Tran van Trung 30 77639133 Martirosyan-Tran van Trung 32 78206136 Martirosyan-Tran van Trung 34 78440436 Martirosyan-Tran van Trung 36 99767126 Martirosyan-Tran van Trung 37 131418564 Add 1 factors 38 149827864 Add 2 factors 39 167772110 perfect hash family10,39,17 40 173785350 Add 16 factors 41 176866036 Add 16 factors 42 178586836 Add 16 factors 43 182048236 Add 16 factors 44 182487436 Add 16 factors 45 189008733 Add 16 factors 46 191979693 Add 16 factors 47 192546696 Add 16 factors 48 193594056 Add 16 factors 49 193889796 Add 16 factors 50 194026836 Add 16 factors 52 199675633 perfect hash family16,65,13S3 56 200579142 perfect hash family16,65,13S2 60 201482651 perfect hash family16,65,13T1 65 202386160 perfect hash family16,65,13 66 217954320 perfect hash family16,66,14 112 240039782 Power CT16^2Arc(18):9 twos,0 ones 116 246349914 Power CT16^2Arc(14):7 twos,0 ones 124 249504980 Power CT16^2Arc(12):6 twos,0 ones 128 251687036 Power CT16^2TD(4):3,2,2,2,2 136 252660046 Power CT16^2TD(4):2,2,2,2,2 142 254842102 Power CT16^2TD(4):3,2,2,2,0 152 255815112 Power CT16^2TD(4):2,2,2,2,0 160 257997168 Power CT16^2TD(2):2,2,3 172 258970178 Power CT16^2TD(2):2,2,2 182 261152234 Power CT16^2T3T2 196 262125244 Power CT16^2T2T2 204 263403791 Power CT17^2T5 221 264307300 Power CT17^2T4 238 265280310 Power CT17^2T3 256 268435212 perfect hash family16,256,16,c fuse fuse 289 268435376 Power CT17^2 290 327966484 Add 1 factors 291 352985296 Add 2 factors 292 383964034 Add 3 factors 293 426299216 Add 4 factors 294 432780176 Add 5 factors 305 442027856 Add 16 factors 306 479922448 Add 17 factors 320 530221148 perfect hash family32,512,16T6 352 531000194 perfect hash family32,512,16T5 384 531839167 perfect hash family32,512,16T4 416 532742676 perfect hash family32,512,16T3 448 533715686 perfect hash family32,512,16T2 512 536870412 perfect hash family32,512,16,c fuse fuse 513 536870752 perfect hash family32,513,17 514 622478456 Add 1 factors 515 654012504 Add 2 factors 516 694326876 Add 3 factors 517 745575712 Add 4 factors 518 752056672 Add 5 factors 519 760197132 Add 16 factors 527 760628172 Add 16 factors 528 761242572 Add 16 factors 529 761304352 Add 16 factors 544 775915992 Martirosyan-Tran van Trung 546 782409350 Martirosyan-Tran van Trung 578 811795142 Martirosyan-Tran van Trung 579 905296186 Add 1 factors 580 916132844 Martirosyan-Tran van Trung 582 956888584 Martirosyan-Tran van Trung 584 1001372086 Martirosyan-Tran van Trung 587 1046712902 Add 16 factors 591 1047020102 Add 16 factors 594 1047251942 Add 16 factors 610 1084921654 Martirosyan-Tran van Trung 626 1090367280 Power CT25^2+1 637 1112908124 Power N-CT29^2Arc(8) 659 1119367981 Power N-CT29^2Arc(7) 682 1125827838 Power N-CT29^2Arc(6) 706 1132287695 Power N-CT29^2Arc(5) 731 1138747552 Power N-CT29^2Arc(4) 757 1145207409 Power N-CT29^2Arc(3) 784 1151667266 Power N-CT29^2T1T1 812 1158127123 Power N-CT29^2T1 842 1164586980 Power N-CT29^2+1 868 1166065165 Power N-CT31^2T3 871 1171391016 Power N-CT31^2Arc(3) 900 1171958019 Power N-CT31^2T1T1 930 1172525022 Power N-CT31^2T1 962 1173092025 Power N-CT31^2+1 964 1176606525 Power N-CT31^2+3 1024 1251298160 Power CT32^2 1026 1255046960 Power CT32^2+2 1027 1364234766 Add 1 factors 1028 1401726038 Add 2 factors 1029 1448897778 Add 3 factors 1030 1507019360 Add 4 factors 1031 1513500320 Add 5 factors 1037 1517558480 Add 16 factors 1040 1518999200 Add 16 factors 1042 1522748000 Add 16 factors 1043 1575958000 Add 17 factors 1044 1654764065 Power N-CT37^2Arc(10) 1072 1686415503 Power N-CT37^2Arc(9) 1101 1718066941 Power N-CT37^2Arc(8) 1131 1749718379 Power N-CT37^2Arc(7) 1162 1781369817 Power N-CT37^2Arc(6) 1194 1813021255 Power N-CT37^2Arc(5) 1227 1844672693 Power N-CT37^2Arc(4) 1261 1876324131 Power N-CT37^2Arc(3) 1296 1907975569 Power N-CT37^2T1T1 1332 1939627007 Power N-CT37^2T1 1369 1971278445 Power N-CT37^2 1370 2085800489 Add 1 factors 1371 2130846581 Add 2 factors 1425 2147483008 perfect hash family128,1425,17 1452 2223330712 Power CT31^3T20T20T19 1584 2224169685 Power CT31^3T20T19T19 1728 2225008658 Power CT31^3T19T19T19 1872 2225912167 Power CT31^3T19T19T18 2028 2226815676 Power CT31^3T19T18T18 2197 2227719185 Power CT31^3T18T18T18 2366 2228692195 Power CT31^3T18T18T17 2548 2229665205 Power CT31^3T18T17T17 2744 2230638215 Power CT31^3T17T17T17 2873 2231847261 Power CT31^3T18T18T14 3094 2232820271 Power CT31^3T18T17T14 3332 2233793281 Power CT31^3T17T17T14 3468 2235071828 Power CT31^3T19T14T14 3757 2235975337 Power CT31^3T18T14T14 4046 2236948347 Power CT31^3T17T14T14 4913 2240103413 Power CT31^3T14T14T14 5202 2247463764 Power CT31^3T14T14T13 5508 2254824115 Power CT31^3T14T13T13 5832 2262184466 Power CT31^3T13T13T13 6156 2274088904 Power CT31^3T13T13T12 6358 2284024927 Power CT31^3T14T14T9 6480 2284316576 Power CT31^3T13T13T11 6498 2285993342 Power CT31^3T13T12T12 6936 2288762111 Power CT31^3T14T14T7 7514 2291474157 Power CT31^3T14T14T5 8092 2294505477 Power CT31^3T14T14T3 8670 2300965334 Power CT31^3T14T14T1 9248 2301532337 Power CT32^3T15T15 9792 2308892688 Power CT32^3T15T14 10000 2316253039 Power CT31^3T13T13

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