| k | N | Source |
| 20 | 361 | orthogonal array |
| 24 | 520 | orthogonal array |
| 25 | 522 | fuse symbols |
| 26 | 523 | fuse symbols |
| 27 | 524 | fuse symbols |
| 28 | 525 | projection (Colbourn) |
| 29 | 616 | fuse symbols |
| 30 | 617 | fuse symbols |
| 31 | 618 | fuse symbols |
| 32 | 619 | projection (Colbourn) |
| 36 | 649 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 37 | 667 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 38 | 685 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 399 | 703 | CMMSSY 2.3 |
| 400 | 721 | CMMSSY 2.3 |
| 479 | 862 | CMMSSY 2.3 |
| 500 | 864 | CMMSSY 2.3 |
| 520 | 865 | CMMSSY 2.3 |
| 540 | 866 | CMMSSY 2.3 |
| 560 | 867 | CMMSSY 2.2 |
| 580 | 958 | CMMSSY 2.3 |
| 600 | 959 | CMMSSY 2.3 |
| 620 | 960 | CMMSSY 2.3 |
| 640 | 961 | CMMSSY 2.2 |
| 719 | 991 | CMMSSY 2.3 |
| 739 | 1009 | CMMSSY 2.3 |
| 759 | 1027 | CMMSSY 2.3 |
| 784 | 1031 | CMMSSY 2.2 |
| 7961 | 1045 | CMMSSY 2.3 |
| 7980 | 1063 | CMMSSY 2.3 |
| 9557 | 1204 | CMMSSY 2.3 |
| 9975 | 1206 | CMMSSY 2.3 |
| 10374 | 1207 | CMMSSY 2.3 |
| 10773 | 1208 | CMMSSY 2.3 |
| 11200 | 1209 | CMMSSY 2.3 |
| 11571 | 1300 | CMMSSY 2.3 |
| 11970 | 1301 | CMMSSY 2.3 |
| 12369 | 1302 | CMMSSY 2.3 |
| 12800 | 1303 | CMMSSY 2.3 |
| 14345 | 1333 | CMMSSY 2.3 |
| 14744 | 1351 | CMMSSY 2.3 |
| 15143 | 1369 | CMMSSY 2.3 |
| 15680 | 1373 | CMMSSY 2.2 |
| 20000 | 1387 | CMMSSY 2.3 |
| | Graph:
 |