| k | N | Source |
| 4 | 9 | orthogonal array |
| 5 | 11 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 7 | 12 | simulated annealing (Cohen) |
| 9 | 13 | simulated annealing (Cohen) |
| 10 | 14 | simulated annealing (Cohen) |
| 20 | 15 | tabu search (Nurmela) |
| 21 | 16 | tabu search (Zekaoui) |
| 26 | 17 | tabu search (Rouse-Lamarre) |
| 31 | 18 | tabu search (Rouse-Lamarre) |
| 38 | 19 | tabu search (Rouse-Lamarre) |
| 46 | 20 | tabu search (Rouse-Lamarre) |
| 74 | 21 | CMMSSY 2.3 |
| 97 | 23 | CMMSSY 2.3 |
| 134 | 24 | CMMSSY 2.3 |
| 174 | 25 | CMMSSY 2.3 |
| 194 | 26 | CMMSSY 2.2 |
| 394 | 27 | CMMSSY 2.3 |
| 414 | 28 | CMMSSY 2.3 |
| 514 | 29 | CMMSSY 2.3 |
| 614 | 30 | CMMSSY 2.3 |
| 754 | 31 | CMMSSY 2.3 |
| 914 | 32 | CMMSSY 2.3 |
| 1474 | 33 | CMMSSY 2.3 |
| 1828 | 35 | CMMSSY 2.3 |
| 2364 | 36 | CMMSSY 2.2 |
| 3030 | 37 | CMMSSY 2.2 |
| 3766 | 38 | CMMSSY 2.2 |
| 6836 | 39 | CMMSSY 2.2 |
| 7182 | 40 | CMMSSY 2.2 |
| 9026 | 41 | CMMSSY 2.2 |
| 10642 | 42 | CMMSSY 2.2 |
| 13064 | 43 | CMMSSY 2.2 |
| 15832 | 44 | CMMSSY 2.2 |
| 20000 | 45 | CMMSSY 2.2 |