Table for CAN(6,k,10) for k up to 10000

Last Updated Wed Mar 9 06:22:05 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;6,k,10) 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 1000000 composition 8 1229001 Augment OA 9 1357802 Augment OA 10 1494326 Augment OA 12 1771559 orthogonal array fuse 13 2928200 extended OA (Colbourn) special fuse 15 3528479 4-Restricted SCPHF RE (CL) fuse 19 5153619 5-Restricted SCPHF RE (CL) fuse 21 5300029 4-Restricted SCPHF RE (CL) fuse 22 5313339 3-Restricted SCPHF RE (CL) fuse 23 5314679 CPHF IPO 3 (WCS) fuse 26 6764129 5,5-Restricted SCPHF RE (CL) fuse 28 6925169 5-Restricted SCPHF RE (CL) fuse 30 7071579 4-Restricted SCPHF RE (CL) fuse 31 7086099 2-Restricted SCPHF RE (CL) fuse 35 7086239 CPHF IPO 4 (WCS) fuse 41 8696719 5-Restricted SCPHF RE (CL) fuse 43 8843129 4-Restricted SCPHF RE (CL) fuse 44 8856439 3-Restricted SCPHF RE (CL) fuse 45 8857649 2-Restricted SCPHF RE (CL) fuse 46 8857759 SCPHF Random Extension (CLS) fuse 48 8857799 CPHF IPO 5 (WCS) fuse 54 10307229 5,5-Restricted SCPHF RE (CL) fuse 60 10468269 5-Restricted SCPHF RE (CL) fuse 61 10614679 4-Restricted SCPHF RE (CL) fuse 66 10627989 3-Restricted SCPHF RE (CL) fuse 67 10629309 SCPHF Random Extension (CLS) fuse 68 10629359 CPHF Random Extension (CLS) fuse 74 11917739 5,5,5-Restricted SCPHF RE (CL) fuse 83 12078779 5,5-Restricted SCPHF RE (CL) fuse 88 12239819 5-Restricted SCPHF RE (CL) fuse 95 12386229 4-Restricted SCPHF RE (CL) fuse 97 12399539 3-Restricted SCPHF RE (CL) fuse 100 12400749 2-Restricted SCPHF RE (CL) fuse 107 13689289 5,5,5-Restricted SCPHF RE (CL) fuse 121 13850329 5,5-Restricted SCPHF RE (CL) fuse 132 14011369 5-Restricted SCPHF RE (CL) fuse 141 14157779 4-Restricted SCPHF RE (CL) fuse 145 14171089 3-Restricted SCPHF RE (CL) fuse 147 14172299 2-Restricted SCPHF RE (CL) fuse 150 14172409 SCPHF Random Extension (CLS) fuse 208 15943959 SCPHF Random Extension (CLS) fuse 209 22531869 Add 1 factors 210 25780869 Add 2 factors 211 30557459 Add 3 factors 213 31776963 Add 5 factors 214 33037482 Add 6 factors 215 34761659 Add 11 factors 216 34766059 Add 11 factors 217 34792679 Add 11 factors 219 34805989 Add 11 factors 220 41393899 Add 11 factors 250 43441171 SCPHF Random Extension (CLS) fuse fuse fuse 251 51104581 Add 1 factors 252 54353581 Add 2 factors 253 59473211 Add 3 factors 264 60383587 Martirosyan-TVT 266 60529997 Martirosyan-TVT 267 62004172 perfect hash family4,328,208T61 270 62004282 perfect hash family4,328,208T58 328 63775832 perfect hash family4,328,208 335 70599150 Martirosyan-TVT variant 339 70742828 Martirosyan-TVT variant 340 72035930 Martirosyan-TVT 341 72288930 Martirosyan-TVT variant 343 73271320 Martirosyan-TVT variant 347 73417198 Martirosyan-TVT variant 364 73563076 Martirosyan-TVT 365 73682866 Martirosyan-TVT variant 381 74558134 Martirosyan-TVT variant 386 74704012 Martirosyan-TVT 387 74730852 Martirosyan-TVT variant 391 74757692 Martirosyan-TVT variant 392 75634280 Martirosyan-TVT 398 75645170 Martirosyan-TVT 399 75672670 Martirosyan-TVT variant 406 75700170 Martirosyan-TVT 407 75710170 Martirosyan-TVT variant 409 75720170 Martirosyan-TVT variant 411 76012966 Martirosyan-TVT variant 416 76159364 Martirosyan-TVT 476 79719790 perfect hash family5,476,208 483 85020198 Power CT23^2T2 484 85032168 Power CT23^2T1T1 506 85033508 Power CT23^2T1 529 85034848 Power CT23^2 530 94123858 Add 1 factors 568 95663748 perfect hash family6,568,208 578 103716709 perfect hash familyD16,578,34^11 17^5 581 103731130 Power N-CT29^2Arc(4)T6 601 103877540 Power N-CT29^2Arc(3)T6 622 104023950 Power N-CT29^2Arc(2)T6 644 104170360 Power N-CT29^2T6T1 667 104316770 Power N-CT29^2T6 668 104491010 Power N-CT31^2Arc(2)T8 690 104505530 Power N-CT31^2T8T1 713 104520050 Power N-CT31^2T8 731 105488030 Power N-CT29^2Arc(4) 757 105634440 Power N-CT29^2Arc(3) 784 105780850 Power N-CT29^2T1T1 812 105927260 Power N-CT29^2T1 842 106073670 Power N-CT29^2+1 868 106130540 Power N-CT31^2T3 871 106247910 Power N-CT31^2Arc(3) 900 106262430 Power N-CT31^2T1T1 930 106276950 Power N-CT31^2T1 961 106291470 Power N-CT31^2 965 106293570 perfect hash family15,965,35 992 113379668 Power CT32^2T1 1027 113379808 Power CT32^2+3 1051 116922612 Power N-CT41^2Trin6,6,6 1085 118532952 Power N-CT41^2T10T6 1225 118533092 Power N-CT41^2T6T6 1230 120128912 Power N-CT41^2T11 1271 120143432 Power N-CT41^2T10 1435 120143572 Power N-CT41^2T6 1681 121754052 Power N-CT41^2 1763 123657382 Power N-CT43^2T2 1849 123803792 Power N-CT43^2 1886 123848052 Power N-CT47^2T6T1 1927 123848092 Power N-CT47^2T6 1935 123994352 Power N-CT47^2T4T2 1936 123994422 Power N-CT47^2Arc(2)T4 1978 123994462 Power N-CT47^2T4T1 2021 123994502 Power N-CT47^2T4 2024 124007772 Power N-CT47^2T3T1 2068 124007812 Power N-CT47^2T3 2070 124008982 Power N-CT47^2T2T1 2115 124009022 Power N-CT47^2T2 2116 124009092 Power N-CT47^2T1T1 2162 124009132 Power N-CT47^2T1 2210 124009172 Power N-CT47^2+1 2211 135860282 Add 1 factors 2304 141402332 Power N-CT53^2T5T5 2332 142850402 Power N-CT53^2T9 2385 142851612 Power N-CT53^2T8 2438 142851722 Power N-CT53^2T7 2544 142851762 Power N-CT53^2T5 2810 144301192 Power N-CT53^2+1 2832 144945282 Power N-CT59^2T11 2916 146233672 Power N-CT59^2T5T5 3186 146394712 Power N-CT59^2T5 3482 146555752 Power N-CT59^2+1 3483 148019852 Power N-CT61^2Arc(4) 3541 148166262 Power N-CT61^2Arc(3) 3600 148312672 Power N-CT61^2T1T1 3660 148459082 Power N-CT61^2T1 3721 148605492 Power N-CT61^2 3730 148642672 Power N-CT67^2Arc(5)T7 3786 148643992 Power N-CT67^2Arc(4)T7 3843 148645312 Power N-CT67^2Arc(3)T7 3901 148646632 Power N-CT67^2Arc(2)T7 3960 148647952 Power N-CT67^2T7T1 4020 148649272 Power N-CT67^2T7 4026 148794362 Power N-CT67^2T6T1 4087 148795682 Power N-CT67^2T6 4102 148802392 Power N-CT67^2Arc(6) 4164 148803712 Power N-CT67^2Arc(5) 4227 148805032 Power N-CT67^2Arc(4) 4291 148806352 Power N-CT67^2Arc(3) 4356 148807672 Power N-CT67^2T1T1 4422 148808992 Power N-CT67^2T1 4489 148810312 Power N-CT67^2 4490 148811012 Power N-CT67^2+1 4556 152353784 Power N-CT73^2T6T5 4624 152353834 Power N-CT73^2T5T5 4818 153640844 Power N-CT73^2T7 4891 153642164 Power N-CT73^2T6 4964 153642214 Power N-CT73^2T5 5330 154930594 Power N-CT73^2+1 5478 155573324 Power N-CT83^2T17 5561 155574644 Power N-CT83^2T16 5644 155574694 Power N-CT83^2T15 6142 156863074 Power N-CT83^2T9 6889 157024114 Power N-CT83^2 6894 159117634 perfect hash family13,6894,88 6919 159264044 Power N-CT89^2Arc(12) 6997 159410454 Power N-CT89^2Arc(11) 7076 159556864 Power N-CT89^2Arc(10) 7382 159599214 Power N-CT101^2Arc(13)T18 7822 159760254 Power N-CT101^2Arc(13)T13 8438 159906664 Power N-CT101^2Arc(13)T6 8614 159919974 Power N-CT101^2Arc(13)T4 8790 159921184 Power N-CT101^2Arc(13)T2 8839 161154064 Power N-CT97^2Trin2,2,2 9025 161167374 Power N-CT97^2T2T2 9215 161180684 Power N-CT97^2T2 9409 161193994 Power N-CT97^2 9412 161209724 Power N-CT97^2+3 9421 167652424 Power N-CT101^2Arc(8) 9515 168940964 Power N-CT101^2Arc(7) 9610 170229504 Power N-CT101^2Arc(6) 9706 171518044 Power N-CT101^2Arc(5) 9803 172806584 Power N-CT101^2Arc(4) 9901 174095124 Power N-CT101^2Arc(3) 10000 175383664 Power N-CT101^2T1T1

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