| k | N | Source |
| 12 | 1771561 | orthogonal array |
| 13 | 3367430 | extended OA (Colbourn) |
| 14 | 4826805 | orthogonal array fuse fuse |
| 15 | 7086240 | perfect hash family4,15,12 |
| 24 | 8696754 | Martirosyan-Tran van Trung |
| 25 | 11916564 | Add a factor |
| 26 | 16587274 | Add a factor |
| 28 | 21786773 | Martirosyan-Tran van Trung |
| 29 | 24801840 | perfect hash family14,29,12 |
| 33 | 26573400 | perfect hash family15,33,12 |
| 36 | 28344960 | perfect hash family16,36,12 |
| 37 | 30116520 | perfect hash family17,37,12 |
| 38 | 30500987 | Martirosyan-Tran van Trung |
| 40 | 31086407 | Martirosyan-Tran van Trung |
| 42 | 31671827 | Martirosyan-Tran van Trung |
| 44 | 32081621 | Martirosyan-Tran van Trung |
| 46 | 32725583 | Martirosyan-Tran van Trung |
| 48 | 38766603 | Martirosyan-Tran van Trung |
| 49 | 40745880 | perfect hash family23,49,12 |
| 50 | 42517440 | perfect hash family24,50,12 |
| 52 | 44289000 | perfect hash family25,52,12 |
| 55 | 46060560 | perfect hash family26,55,12 |
| 59 | 47832120 | perfect hash family27,59,12 |
| 60 | 52282995 | perfect hash family16,65,13T1 |
| 65 | 53878864 | perfect hash family16,65,13 |
| 66 | 61492074 | Add a factor |
| 67 | 69105284 | Add a factor |
| 68 | 75983793 | Martirosyan-Tran van Trung |
| 72 | 76064973 | Martirosyan-Tran van Trung |
| 74 | 77935753 | Martirosyan-Tran van Trung |
| 76 | 78320220 | Martirosyan-Tran van Trung |
| 80 | 78995840 | Martirosyan-Tran van Trung |
| 84 | 79671460 | Martirosyan-Tran van Trung |
| 88 | 80144394 | Martirosyan-Tran van Trung |
| 92 | 80887576 | Martirosyan-Tran van Trung |
| 96 | 88247596 | Martirosyan-Tran van Trung |
| 98 | 93142973 | Martirosyan-Tran van Trung |
| 100 | 96902573 | Martirosyan-Tran van Trung |
| 101 | 104515783 | Add a factor |
| 104 | 106006623 | Martirosyan-Tran van Trung |
| 110 | 108528193 | Martirosyan-Tran van Trung |
| 112 | 110299753 | Martirosyan-Tran van Trung |
| 118 | 111418653 | Martirosyan-Tran van Trung |
| 120 | 113379840 | RBIBD |
| 128 | 117474417 | Martirosyan-Tran van Trung |
| 130 | 117564617 | Martirosyan-Tran van Trung |
| 132 | 120783473 | Power 16^2T2S9 |
| 133 | 121432394 | Power 16^2S11 |
| 140 | 122393987 | Power 16^2T2S8 |
| 147 | 124004501 | Power 16^2T2S7 |
| 148 | 124653422 | Power 16^2S9 |
| 155 | 125615015 | Power 16^2T2S6 |
| 156 | 126263936 | Power 16^2S8 |
| 164 | 127225529 | Power 16^2T2S5 |
| 165 | 127874450 | perfect hash family16,256,16S7 |
| 168 | 128352906 | Power 16^2T4T2 |
| 169 | 128489400 | Power 16^2T3T3 |
| 174 | 128836043 | Power 16^2T2S4 |
| 175 | 129484964 | perfect hash family16,256,16S6 |
| 182 | 129948775 | Power 16^2T3T2 |
| 185 | 130446557 | Power 16^2T2S3 |
| 186 | 131095478 | perfect hash family16,256,16S5 |
| 196 | 131408150 | Power 16^2T2T2 |
| 197 | 132057071 | Power 16^2T2S2 |
| 276 | 132222855 | Power 23^2T11 |
| 299 | 133818724 | Power 23^2T10 |
| 322 | 135278099 | Power 23^2T9 |
| 345 | 137537534 | Power 23^2T8 |
| 530 | 139148048 | Power 23^2+1 |
| 531 | 155546958 | Add a factor |
| 532 | 171945868 | Add a factor |
| 553 | 181005578 | Power 25^2S3 |
| 576 | 184225388 | Power 25^2T1T1 |
| 600 | 187445198 | Power 25^2T1 |
| 625 | 190665008 | Power 25^2 |
| 626 | 208273918 | Add a factor |
| 627 | 225882828 | Add a factor |
| 628 | 243491738 | Add a factor |
| 629 | 261100648 | Add a factor |
| 630 | 278709558 | Add a factor |
| 644 | 295471955 | Martirosyan-Tran van Trung |
| 668 | 297731390 | Martirosyan-Tran van Trung |
| 690 | 297740410 | Martirosyan-Tran van Trung |
| 704 | 299350924 | Martirosyan-Tran van Trung |
| 764 | 299955924 | Martirosyan-Tran van Trung |
| 768 | 300010044 | Martirosyan-Tran van Trung |
| 796 | 300046124 | Martirosyan-Tran van Trung |
| 812 | 302122121 | Martirosyan-Tran van Trung |
| 838 | 302212321 | Martirosyan-Tran van Trung |
| 840 | 314830201 | Martirosyan-Tran van Trung |
| 860 | 319050681 | Martirosyan-Tran van Trung |
| 864 | 319131861 | Martirosyan-Tran van Trung |
| 908 | 319140881 | Martirosyan-Tran van Trung |
| 968 | 319231081 | Martirosyan-Tran van Trung |
| 976 | 319474071 | Martirosyan-Tran van Trung |
| 1060 | 320562731 | Martirosyan-Tran van Trung |
| 1061 | 338171641 | Add a factor |
| 1062 | 343749741 | Martirosyan-Tran van Trung |
| 1063 | 361358651 | Add a factor |
| 1064 | 366889481 | Martirosyan-Tran van Trung |
| 1084 | 375949191 | Martirosyan-Tran van Trung |
| 1088 | 376003311 | Martirosyan-Tran van Trung |
| 1100 | 376113631 | Martirosyan-Tran van Trung |
| 1106 | 386519994 | Martirosyan-Tran van Trung |
| 1144 | 389739804 | Martirosyan-Tran van Trung |
| 1152 | 390282404 | Martirosyan-Tran van Trung |
| 1160 | 393808894 | Martirosyan-Tran van Trung |
| 1200 | 393826934 | Martirosyan-Tran van Trung |
| 1204 | 408218424 | Martirosyan-Tran van Trung |
| 1232 | 408928581 | Martirosyan-Tran van Trung |
| 1248 | 410018281 | Martirosyan-Tran van Trung |
| 1250 | 410045341 | Martirosyan-Tran van Trung |
| 1251 | 427654251 | Add a factor |
| 1253 | 436380524 | Power N41^2S12 |
| 1257 | 436550877 | Power N41^2T8S3 |
| 1275 | 436566177 | Power N41^2T5S6 |
| 1296 | 436751830 | Power N41^2T5T5 |
| 1306 | 437151597 | Power N41^2T5S5 |
| 1316 | 437551364 | Power N41^2S10 |
| 1320 | 437721717 | Power N41^2T8T1 |
| 1338 | 437737017 | Power N41^2T5S4 |
| 1348 | 438136784 | Power N41^2S9 |
| 1353 | 438307137 | Power N41^2T8 |
| 1371 | 438322437 | Power N41^2T5S3 |
| 1381 | 438722204 | Power N41^2S8 |
| 1405 | 438907857 | Power N41^2T5S2 |
| 1415 | 439307624 | Power N41^2S7 |
| 1440 | 439493277 | Power N41^2T5T1 |
| 1450 | 439893044 | Power N41^2S6 |
| 1476 | 440078697 | Power N41^2T5 |
| 1486 | 440478464 | Power N41^2S5 |
| 1523 | 441063884 | Power N41^2S4 |
| 1561 | 441649304 | Power N41^2S3 |
| 1600 | 442234724 | Power N41^2T1T1 |
| 1640 | 442820144 | Power N41^2T1 |
| 1682 | 443405564 | Power N41^2+1 |
| 1683 | 447503504 | Power N43^2S4 |
| 1723 | 447913298 | Power N43^2S3 |
| 1764 | 448323092 | Power N43^2T1T1 |
| 1806 | 448732886 | Power N43^2T1 |
| 1850 | 449142680 | Power N43^2+1 |
| 1852 | 458158148 | Power N43^2+3 |
| 1853 | 481423478 | Add a factor |
| 1861 | 494404268 | Power N47^2S8 |
| 1901 | 500445288 | Power N47^2S7 |
| 1942 | 506486308 | Power N47^2S6 |
| 1984 | 512527328 | Power N47^2S5 |
| 2027 | 518568348 | Power N47^2S4 |
| 2071 | 524609368 | Power N47^2S3 |
| 2116 | 530650388 | Power N47^2T1T1 |
| 2162 | 536691408 | Power N47^2T1 |
| 2210 | 542732428 | Power N47^2+1 |
| 2211 | 567940798 | Add a factor |
| 2212 | 593149168 | Add a factor |
| 2213 | 618357538 | Add a factor |
| 2218 | 622655049 | Power N53^2T7S5 |
| 2238 | 623589106 | Power N53^2S12 |
| 2260 | 624426609 | Power N53^2T7S4 |
| 2281 | 625360666 | Power N53^2S11 |
| 2303 | 626198169 | Power N53^2T7S3 |
| 2324 | 627132226 | Power N53^2S10 |
| 2347 | 627969729 | Power N53^2T7S2 |
| 2368 | 628903786 | Power N53^2S9 |
| 2392 | 629741289 | Power N53^2T7T1 |
| 2413 | 630675346 | Power N53^2S8 |
| 2438 | 631512849 | Power N53^2T7 |
| 2459 | 632446906 | Power N53^2S7 |
| 2506 | 634218466 | Power N53^2S6 |
| 2554 | 635990026 | Power N53^2S5 |
| 2603 | 637761586 | Power N53^2S4 |
| 2653 | 639533146 | Power N53^2S3 |
| 2704 | 641304706 | Power N53^2T1T1 |
| 2756 | 643076266 | Power N53^2T1 |
| 2811 | 644847826 | Power N53^2+2 |
| 2832 | 660584149 | Power N59^2T11 |
| 2891 | 662563426 | Power N59^2T10 |
| 2950 | 664334986 | Power N59^2T9 |
| 3068 | 666106546 | Power N59^2T7 |
| 3245 | 667878106 | Power N59^2T4 |
| 3481 | 669649666 | Power N59^2 |
| 3482 | 699662176 | Add a factor |
| 3483 | 729674686 | Add a factor |
| 3540 | 746661469 | Power N61^2T2T1 |
| 3599 | 748257338 | Power N61^2T2 |
| 3600 | 751112344 | Power N61^2T1T1 |
| 3660 | 752708213 | Power N61^2T1 |
| 3724 | 754304082 | Power N61^2+3 |
| 4608 | 774171691 | Power 32^3T20T20 |
| 4992 | 775767560 | Power 32^3T20T19 |
| 5376 | 777226935 | Power 32^3T20T18 |
| 5408 | 777363429 | Power 32^3T19T19 |
| 5824 | 778822804 | Power 32^3T19T18 |
| 6272 | 780282179 | Power 32^3T18T18 |
| 9216 | 781096884 | Power 32^3T20T8 |
| 9984 | 782692753 | Power 32^3T19T8 |
| 10000 | 784152128 | Power 31^3T17T7 |