| k | N | Source |
| 17 | 16777216 | orthogonal array |
| 18 | 24137567 | orthogonal array fuse |
| 19 | 39866207 | Add a factor |
| 20 | 47045875 | orthogonal array fuse fuse fuse |
| 21 | 67108816 | perfect hash family4,21,16,c |
| 23 | 67108860 | perfect hash family4,23,17 |
| 32 | 79691776 | double OA (Colbourn-Zhou) |
| 34 | 80736256 | double OA (Colbourn-Zhou) |
| 36 | 109985476 | Martirosyan-Tran van Trung |
| 37 | 157912756 | Add a factor |
| 39 | 167772150 | perfect hash family10,39,17 |
| 40 | 184549216 | perfect hash family11,40,16,c |
| 44 | 184549365 | perfect hash family11,44,17 |
| 50 | 201326580 | perfect hash family12,50,17 |
| 53 | 218103795 | perfect hash family13,53,17 |
| 60 | 234881010 | perfect hash family14,60,17 |
| 80 | 251658016 | perfect hash family15,80,16,c |
| 85 | 251658225 | Power CT17^2Tlev |
| 256 | 268435216 | perfect hash family16,256,16,c |
| 289 | 268435440 | Power CT17^2 |
| 290 | 359443200 | Add a factor |
| 291 | 456061200 | Add a factor |
| 292 | 469762020 | perfect hash family28,292,17 |
| 293 | 520093665 | perfect hash family31,293,17 |
| 512 | 536870416 | perfect hash family32,512,16,c |
| 513 | 536870880 | perfect hash family32,513,17 |
| 514 | 662392800 | Add a factor |
| 516 | 754974675 | perfect hash family45,516,17 |
| 517 | 880496595 | Add a factor |
| 518 | 905969610 | perfect hash family54,518,17 |
| 544 | 938450763 | Martirosyan-Tran van Trung |
| 576 | 967090799 | Martirosyan-Tran van Trung |
| 578 | 971984881 | perfect hash familyD16,578,34^11 17^5 |
| 579 | 1130421361 | Add a factor |
| 589 | 1155551056 | Power N-CT31^2T12 |
| 620 | 1162730724 | Power N-CT31^2T11 |
| 651 | 1182793665 | Power N-CT31^2T10 |
| 713 | 1182793709 | Power N-CT31^2T8 |
| 962 | 1195376625 | Power N-CT31^2+1 |
| 964 | 1211043825 | Power N-CT31^2+3 |
| 1024 | 1275068400 | Power CT32^2 |
| 1026 | 1291780080 | Power CT32^2+2 |
| 1027 | 1468788720 | Add a factor |
| 1028 | 1645797360 | Add a factor |
| 1029 | 1822806000 | Add a factor |
| 1056 | 1879048080 | perfect hash family112,1056,17 |
| 1072 | 1937345805 | Power N-CT37^2Arc(9) |
| 1101 | 1985273085 | Power N-CT37^2Arc(8) |
| 1131 | 2033200365 | Power N-CT37^2Arc(7) |
| 1162 | 2081127645 | Power N-CT37^2Arc(6) |
| 1194 | 2129054925 | Power N-CT37^2Arc(5) |
| 1425 | 2147483520 | perfect hash family128,1425,17 |
| 4913 | 2281701345 | Power CT31^3T14T14T14 |
| 5202 | 2289061696 | Power CT31^3T14T14T13 |
| 5508 | 2296422047 | Power CT31^3T14T13T13 |
| 5832 | 2303782398 | Power CT31^3T13T13T13 |
| 6120 | 2319330355 | Power CT31^3T14T13T11 |
| 6156 | 2319511038 | Power CT31^3T13T13T12 |
| 6480 | 2326690706 | Power CT31^3T13T13T11 |
| 6647 | 2332032989 | Power CT31^3T14T14T8 |
| 7038 | 2339393340 | Power CT31^3T14T13T8 |
| 9248 | 2344615905 | Power CT32^3T15T15 |
| 9792 | 2351976256 | Power CT32^3T15T14 |
| 10000 | 2359336607 | Power CT31^3T13T13 |