| k | N | Source |
| 7 | 85766121 | composition |
| 8 | 104772459 | Add a symbol |
| 9 | 115801137 | Add a symbol |
| 10 | 127990730 | Add a symbol |
| 11 | 141463438 | Add a symbol |
| 24 | 148035885 | orthogonal array fuse fuse |
| 26 | 244140617 | orthogonal array fuse fuse fuse fuse |
| 28 | 387420477 | orthogonal array fuse fuse fuse fuse fuse fuse |
| 31 | 592143483 | perfect hash family4,31,23,c fuse fuse |
| 32 | 688248268 | perfect hash family4,35,25S3 |
| 48 | 716316374 | Martirosyan-Tran van Trung |
| 49 | 985819034 | Add a factor |
| 50 | 1091776651 | Martirosyan-Tran van Trung |
| 52 | 1093339119 | Martirosyan-Tran van Trung |
| 53 | 1465823259 | Add a factor |
| 54 | 1480358679 | perfect hash family10,54,23,c fuse fuse |
| 55 | 1480358840 | perfect hash family10,55,24 |
| 63 | 1628394545 | perfect hash family11,63,23,c fuse fuse |
| 64 | 1628394724 | perfect hash family11,64,24 |
| 67 | 1776430411 | perfect hash family12,67,23,c fuse fuse |
| 68 | 1776430608 | perfect hash family12,68,24 |
| 69 | 1924466492 | perfect hash family13,69,24 |
| 72 | 2072502376 | perfect hash family14,72,24 |
| 115 | 2220538009 | perfect hash family15,115,23,c fuse fuse |
| 161 | 2306304380 | Power 23^2T16 |
| 184 | 2325310718 | Power 23^2T15 |
| 207 | 2336339396 | Power 23^2T14 |
| 230 | 2348528989 | Power 23^2T13 |
| 253 | 2362001697 | Power 23^2T12 |
| 529 | 2368573875 | perfect hash family16,529,23,c fuse fuse |
| 530 | 2368574144 | Power 23^2+1 |
| 531 | 2940907724 | Add a factor |
| 532 | 3523017224 | Add a factor |
| 553 | 3617935660 | Power 25^2S3 |
| 576 | 3714040392 | Power 25^2T1T1 |
| 600 | 3810145124 | Power 25^2T1 |
| 625 | 3906249617 | perfect hash family16,625,25,c fuse fuse fuse fuse |
| 626 | 3906249856 | Power 25^2+1 |
| 627 | 4682953756 | Add a factor |
| 628 | 5459657656 | Add a factor |
| 651 | 5768888036 | Power 27^2S3 |
| 676 | 5912167896 | Power 27^2T1T1 |
| 702 | 6055447756 | Power 27^2T1 |
| 730 | 6198727616 | Power 27^2+1 |
| 731 | 7074559076 | Add a factor |
| 735 | 7253757453 | perfect hash family49,735,23,c fuse fuse |
| 744 | 7697865051 | perfect hash family52,744,23,c fuse fuse |
| 1058 | 7703738314 | Martirosyan-Tran van Trung |
| 1060 | 7751454383 | Martirosyan-Tran van Trung |
| 1062 | 8621290763 | Martirosyan-Tran van Trung |
| 1128 | 9460148733 | Power N47^2T23 |
| 1222 | 9556253465 | Power N47^2T21 |
| 1316 | 9699533325 | Power N47^2T19 |
| 1457 | 9904256331 | Power N47^2T16 |
| 1504 | 10000361116 | Power N47^2T15 |
| 2210 | 10028429222 | Power N47^2+1 |
| 2211 | 11378170202 | Add a factor |
| 2212 | 12727911182 | Add a factor |
| 2213 | 14077652162 | Add a factor |
| 2257 | 14964596548 | Power 49^2S3 |
| 2304 | 15234099208 | Power 49^2T1T1 |
| 2352 | 15503601868 | Power 49^2T1 |
| 2401 | 15773104528 | Power 49^2 |
| 2402 | 17122845508 | Add a factor |
| 2511 | 17403763250 | Power 31^3T22T22 |
| 5208 | 17405962982 | Power 31^3T24T7 |
| 5952 | 17424969320 | Power 31^3T23T7 |
| 6696 | 17435997998 | Power 31^3T22T7 |
| 7440 | 17448187591 | Power 31^3T21T7 |
| 8184 | 17461660299 | Power 31^3T20T7 |
| 10000 | 17468232746 | Power 31^3T7T7 |