| k | N | Source |
| 5 | 16 | orthogonal array |
| 6 | 19 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 7 | 21 | simulated annealing (Cohen) |
| 8 | 22 | simulated annealing (Cohen) |
| 9 | 23 | tabu search (Rouse-Lamarre) |
| 12 | 24 | simulated annealing (CKRS) |
| 13 | 25 | simulated annealing (CKRS) |
| 15 | 27 | tabu search (Rouse-Lamarre) |
| 24 | 28 | CMMSSY 2.3 |
| 29 | 31 | CMMSSY 2.3 |
| 30 | 32 | CMMSSY 2.3 |
| 34 | 33 | CMMSSY 2.3 |
| 38 | 34 | CMMSSY 2.3 |
| 42 | 35 | CMMSSY 2.3 |
| 50 | 36 | CMMSSY 2.3 |
| 54 | 37 | CMMSSY 2.3 |
| 60 | 38 | CMMSSY 2.3 |
| 69 | 39 | CMMSSY 2.3 |
| 116 | 40 | CMMSSY 2.3 |
| 140 | 43 | CMMSSY 2.3 |
| 144 | 44 | CMMSSY 2.3 |
| 164 | 45 | CMMSSY 2.3 |
| 184 | 46 | CMMSSY 2.3 |
| 204 | 47 | CMMSSY 2.3 |
| 248 | 48 | CMMSSY 2.3 |
| 268 | 49 | CMMSSY 2.3 |
| 292 | 50 | CMMSSY 2.3 |
| 332 | 51 | CMMSSY 2.3 |
| 560 | 52 | CMMSSY 2.3 |
| 676 | 55 | CMMSSY 2.3 |
| 696 | 56 | CMMSSY 2.3 |
| 792 | 57 | CMMSSY 2.3 |
| 888 | 58 | CMMSSY 2.3 |
| 984 | 59 | CMMSSY 2.3 |
| 1192 | 60 | CMMSSY 2.3 |
| 1288 | 61 | CMMSSY 2.3 |
| 1408 | 62 | CMMSSY 2.3 |
| 1604 | 63 | CMMSSY 2.3 |
| 2704 | 64 | CMMSSY 2.3 |
| 3264 | 67 | CMMSSY 2.3 |
| 3360 | 68 | CMMSSY 2.3 |
| 3824 | 69 | CMMSSY 2.3 |
| 4288 | 70 | CMMSSY 2.3 |
| 4752 | 71 | CMMSSY 2.3 |
| 5760 | 72 | CMMSSY 2.3 |
| 6224 | 73 | CMMSSY 2.3 |
| 6800 | 74 | CMMSSY 2.3 |
| 7744 | 75 | CMMSSY 2.3 |
| 13056 | 76 | CMMSSY 2.3 |
| 15760 | 79 | CMMSSY 2.3 |
| 16224 | 80 | CMMSSY 2.3 |
| 18464 | 81 | CMMSSY 2.3 |
| 19936 | 82 | CMMSSY 2.2 |
| 20000 | 83 | CMMSSY 2.2 |