| k | N | Source |
| 7 | 64000000 | composition |
| 8 | 70914127 | Add a symbol |
| 9 | 74646449 | Add a symbol |
| 10 | 78575209 | Add a symbol |
| 11 | 82710746 | Add a symbol |
| 12 | 87063943 | Add a symbol |
| 13 | 91646255 | Add a symbol |
| 14 | 96469742 | Add a symbol |
| 15 | 101547096 | Add a symbol |
| 16 | 106891680 | Add a symbol |
| 17 | 112517557 | Add a symbol |
| 18 | 118439533 | Add a symbol |
| 19 | 124673192 | Add a symbol |
| 20 | 131234938 | Add a symbol |
| 24 | 148035883 | orthogonal array fuse fuse fuse |
| 26 | 244140615 | orthogonal array fuse fuse fuse fuse fuse |
| 28 | 387420475 | orthogonal array fuse fuse fuse fuse fuse fuse fuse |
| 29 | 589362735 | Add a factor |
| 31 | 592143481 | perfect hash family4,31,23,c fuse fuse fuse |
| 32 | 646849011 | Martirosyan-Tran van Trung |
| 34 | 658100750 | Martirosyan-Tran van Trung |
| 36 | 669944684 | Martirosyan-Tran van Trung |
| 38 | 680029339 | Martirosyan-Tran van Trung |
| 40 | 686591085 | Martirosyan-Tran van Trung |
| 48 | 703392030 | Martirosyan-Tran van Trung |
| 49 | 947227010 | Add a factor |
| 50 | 1075696810 | Martirosyan-Tran van Trung |
| 52 | 1078040500 | Martirosyan-Tran van Trung |
| 53 | 1371405101 | perfect hash family11,53,19 |
| 54 | 1421274384 | perfect hash family12,54,18 |
| 55 | 1430460815 | perfect hash family11,60,20S2 |
| 57 | 1437022561 | perfect hash family11,60,20T1 |
| 60 | 1443584307 | perfect hash family11,60,20 |
| 65 | 1466340064 | perfect hash family16,65,13 |
| 66 | 1543515856 | perfect hash family16,66,14 |
| 67 | 1587341433 | perfect hash family15,80,16S3 |
| 71 | 1592686017 | perfect hash family15,80,16S2 |
| 75 | 1598030601 | perfect hash family15,80,16T1 |
| 76 | 1601781633 | Power 16^2T6S15 |
| 80 | 1603375185 | Power 16^2Tlev |
| 82 | 1605917170 | Power 16^2T5S15 |
| 88 | 1610270367 | Power 16^2T4S15 |
| 94 | 1614852679 | Power 16^2T3S15 |
| 100 | 1619676166 | Power 16^2T2S15 |
| 106 | 1624753520 | Power 16^2S16 |
| 111 | 1630098104 | Power 16^2S15 |
| 117 | 1635442688 | Power 16^2S14 |
| 122 | 1640787272 | Power 16^2S13 |
| 127 | 1646131856 | Power 16^2S12 |
| 133 | 1651476440 | Power 16^2S11 |
| 140 | 1656821024 | Power 16^2S10 |
| 148 | 1662165608 | Power 16^2S9 |
| 156 | 1667510192 | Power 16^2S8 |
| 165 | 1672854776 | Power 16^2S7 |
| 175 | 1678199360 | Power 16^2S6 |
| 186 | 1683543944 | Power 16^2S5 |
| 198 | 1688888528 | Power 16^2S4 |
| 211 | 1694233112 | Power 16^2S3 |
| 225 | 1699577696 | Power 16^2T1T1 |
| 240 | 1704922280 | Power 16^2T1 |
| 256 | 1710266864 | Power 16^2 |
| 272 | 1794655019 | Power 17^2T1 |
| 289 | 1800280896 | Power 17^2 |
| 290 | 1895032512 | Power 17^2+1 |
| 291 | 1969836420 | Power 19^2S4 |
| 307 | 1976070079 | Power 19^2S3 |
| 324 | 1982303738 | Power 19^2T1T1 |
| 342 | 1988537397 | Power 19^2T1 |
| 361 | 1994771056 | Power 19^2 |
| 362 | 2099758992 | Power 19^2+1 |
| 368 | 2327429909 | Power 23^2T7 |
| 380 | 2328410476 | Power 23^2T4T3 |
| 391 | 2333055786 | Power 23^2T6 |
| 400 | 2334972222 | Power 23^2T3T3 |
| 414 | 2338977762 | Power 23^2T5 |
| 437 | 2345211421 | Power 23^2T4 |
| 460 | 2351773167 | Power 23^2T3 |
| 529 | 2368573873 | perfect hash family16,529,23,c fuse fuse fuse |
| 530 | 2368574112 | Power 23^2+1 |
| 531 | 2886398972 | Add a factor |
| 532 | 3413068712 | Add a factor |
| 553 | 3617935628 | Power 25^2S3 |
| 576 | 3714040360 | Power 25^2T1T1 |
| 600 | 3810145092 | Power 25^2T1 |
| 625 | 3906249615 | perfect hash family16,625,25,c fuse fuse fuse fuse fuse |
| 626 | 3906249824 | Power 25^2+1 |
| 627 | 4608981164 | Add a factor |
| 628 | 5311712504 | Add a factor |
| 651 | 5768888004 | Power 27^2S3 |
| 676 | 5912167864 | Power 27^2T1T1 |
| 702 | 6055447724 | Power 27^2T1 |
| 730 | 6198727584 | Power 27^2+1 |
| 731 | 6991145764 | Add a factor |
| 735 | 7253757451 | perfect hash family49,735,23,c fuse fuse fuse |
| 736 | 7552426793 | Martirosyan-Tran van Trung |
| 760 | 7559033222 | Martirosyan-Tran van Trung |
| 782 | 7563678532 | Martirosyan-Tran van Trung |
| 800 | 7571516926 | Martirosyan-Tran van Trung |
| 828 | 7575522466 | Martirosyan-Tran van Trung |
| 874 | 7585607121 | Martirosyan-Tran van Trung |
| 920 | 7592168867 | Martirosyan-Tran van Trung |
| 1058 | 7608969573 | Martirosyan-Tran van Trung |
| 1060 | 7656266644 | Martirosyan-Tran van Trung |
| 1062 | 8429202984 | Martirosyan-Tran van Trung |
| 1064 | 9210984204 | Martirosyan-Tran van Trung |
| 1128 | 9292132259 | Power N47^2T23 |
| 1222 | 9388236991 | Power N47^2T21 |
| 1316 | 9531516851 | Power N47^2T19 |
| 1348 | 9696279901 | Power N41^2S9 |
| 1381 | 9713080846 | Power N41^2S8 |
| 1415 | 9729881791 | Power N41^2S7 |
| 1457 | 9736239857 | Power N47^2T16 |
| 1486 | 9763483681 | Power N41^2S5 |
| 1523 | 9780284626 | Power N41^2S4 |
| 1561 | 9797085571 | Power N41^2S3 |
| 1598 | 9802197126 | Power N47^2T13 |
| 1600 | 9813886516 | Power N41^2T1T1 |
| 1692 | 9814041060 | Power N47^2T11 |
| 1786 | 9824125715 | Power N47^2T9 |
| 1880 | 9830687461 | Power N47^2T7 |
| 2210 | 9847488406 | Power N47^2+1 |
| 2211 | 11045120726 | Add a factor |
| 2212 | 12242753046 | Add a factor |
| 2213 | 13440385366 | Add a factor |
| 2257 | 14424127204 | Power 49^2S3 |
| 2304 | 14667962184 | Power 49^2T1T1 |
| 2352 | 14911797164 | Power 49^2T1 |
| 2401 | 15155632144 | Power 49^2 |
| 2402 | 16353264464 | Add a factor |
| 2413 | 16852754592 | Power N53^2S8 |
| 2459 | 17146119193 | Power N53^2S7 |
| 2511 | 17321453816 | Power 31^3T22T22 |
| 2604 | 17323224861 | Power 31^3T24T19 |
| 2790 | 17325382576 | Power 31^3T22T21 |
| 2821 | 17327807173 | Power 31^3T24T18 |
| 3100 | 17329311336 | Power 31^3T21T21 |
| 3410 | 17333446873 | Power 31^3T21T20 |
| 3751 | 17337582410 | Power 31^3T20T20 |
| 4092 | 17341935607 | Power 31^3T20T19 |
| 4464 | 17346288804 | Power 31^3T19T19 |
| 4836 | 17350871116 | Power 31^3T19T18 |
| 5239 | 17355453428 | Power 31^3T18T18 |
| 5642 | 17360276915 | Power 31^3T18T17 |
| 6076 | 17365100402 | Power 31^3T17T17 |
| 6510 | 17370177756 | Power 31^3T17T16 |
| 6975 | 17375255110 | Power 31^3T16T16 |
| 7440 | 17380599694 | Power 31^3T16T15 |
| 7936 | 17385944278 | Power 31^3T15T15 |
| 8432 | 17391570155 | Power 31^3T15T14 |
| 8959 | 17397196032 | Power 31^3T14T14 |
| 9486 | 17403118008 | Power 31^3T14T13 |
| 10000 | 17409039984 | Power 31^3T13T13 |