| k | N | Source |
| 20 | 47045881 | orthogonal array |
| 21 | 91485342 | extended OA (Colbourn) |
| 22 | 136055124 | Add a factor |
| 24 | 148035881 | orthogonal array fuse fuse fuse fuse |
| 25 | 188183467 | perfect hash family4,25,19,c |
| 27 | 188183520 | perfect hash family4,27,20 |
| 40 | 232753306 | Martirosyan-Tran van Trung |
| 41 | 337572544 | Add a factor |
| 42 | 423412777 | perfect hash family9,42,19,c |
| 45 | 423412920 | perfect hash family9,45,20 |
| 47 | 470458639 | perfect hash family10,47,19,c |
| 51 | 470458800 | perfect hash family10,51,20 |
| 53 | 517504501 | perfect hash family11,53,19,c |
| 60 | 517504680 | perfect hash family11,60,20 |
| 64 | 564550560 | perfect hash family12,64,20 |
| 65 | 658642320 | perfect hash family14,65,20 |
| 95 | 705687949 | perfect hash family15,95,19,c |
| 96 | 705688200 | perfect hash family15,96,20 |
| 361 | 752733811 | perfect hash family16,361,19,c |
| 362 | 752734080 | Power 19^2+1 |
| 363 | 968545314 | Add a factor |
| 364 | 1193245812 | Add a factor |
| 366 | 1317284155 | perfect hash family28,366,19,c |
| 368 | 1317284640 | perfect hash family28,368,20 |
| 515 | 1505467603 | perfect hash family32,515,19,c |
| 516 | 1505468160 | perfect hash family32,516,20 |
| 517 | 1861532226 | Add a factor |
| 519 | 2070018720 | perfect hash family44,519,20 |
| 520 | 2117063809 | perfect hash family45,520,19,c |
| 522 | 2117064600 | perfect hash family45,522,20 |
| 529 | 2368573871 | perfect hash family16,529,23,c fuse fuse fuse fuse |
| 530 | 2368574080 | Power 23^2+1 |
| 722 | 2479876438 | Martirosyan-Tran van Trung |
| 724 | 2516421459 | Martirosyan-Tran van Trung |
| 726 | 2854460073 | Martirosyan-Tran van Trung |
| 729 | 3010936304 | Power 27^2 |
| 748 | 3213976431 | Power N41^2T16S13 |
| 808 | 3213976484 | Power N41^2T14S13 |
| 1194 | 3258546270 | Power N41^2S14 |
| 1223 | 3363365508 | Power N41^2S13 |
| 1253 | 3468184746 | Power N41^2S12 |
| 1372 | 3491299575 | Power N37^2+3 |
| 1381 | 3887461698 | Power N41^2S8 |
| 1415 | 3992280936 | Power N41^2S7 |
| 1450 | 4097100174 | Power N41^2S6 |
| 1486 | 4201919412 | Power N41^2S5 |
| 1523 | 4306738650 | Power N41^2S4 |
| 1561 | 4411557888 | Power N41^2S3 |
| 1600 | 4516377126 | Power N41^2T1T1 |
| 1640 | 4621196364 | Power N41^2T1 |
| 1681 | 4726015602 | Power N41^2 |
| 1682 | 5233073352 | Add a factor |
| 1720 | 5737121252 | Power N43^2T3 |
| 1722 | 5841940347 | Power N43^2T2T1 |
| 1763 | 5841940490 | Power N43^2T2 |
| 1764 | 5927780580 | Power N43^2T1T1 |
| 1806 | 5927780723 | Power N43^2T1 |
| 1851 | 5927780866 | Power N43^2+2 |
| 1880 | 6348715599 | Power N47^2T7 |
| 1927 | 6453534837 | Power N47^2T6 |
| 2025 | 6492329494 | Power N47^2T2T2 |
| 2115 | 6539375213 | Power N47^2T2 |
| 2209 | 6586420932 | Power N47^2 |
| 2212 | 6586423186 | Power N47^2+3 |
| 2415 | 6774604147 | perfect hash family144,2415,19,c |
| 2416 | 6774606720 | perfect hash family144,2416,20 |
| 10000 | 6843937605 | Power 31^3T11T11 |
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