| k | N | Source |
| 18 | 289 | orthogonal array |
| 20 | 356 | orthogonal array |
| 21 | 358 | fuse symbols |
| 22 | 359 | projection (Colbourn) |
| 31 | 497 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 32 | 513 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 33 | 529 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 34 | 545 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 323 | 561 | CMMSSY 2.3 |
| 324 | 577 | CMMSSY 2.3 |
| 359 | 628 | CMMSSY 2.3 |
| 378 | 630 | CMMSSY 2.3 |
| 396 | 631 | CMMSSY 2.2 |
| 399 | 695 | CMMSSY 2.2 |
| 420 | 697 | CMMSSY 2.2 |
| 440 | 698 | CMMSSY 2.2 |
| 441 | 699 | CMMSSY 2.2 |
| 462 | 700 | CMMSSY 2.2 |
| 484 | 701 | CMMSSY 2.2 |
| 557 | 769 | CMMSSY 2.3 |
| 575 | 785 | CMMSSY 2.3 |
| 593 | 801 | CMMSSY 2.3 |
| 611 | 817 | CMMSSY 2.3 |
| 5797 | 833 | CMMSSY 2.3 |
| 5814 | 849 | CMMSSY 2.3 |
| 6443 | 900 | CMMSSY 2.3 |
| 6783 | 902 | CMMSSY 2.3 |
| 7128 | 903 | CMMSSY 2.3 |
| 7161 | 967 | CMMSSY 2.2 |
| 7539 | 969 | CMMSSY 2.3 |
| 7920 | 970 | CMMSSY 2.2 |
| 7938 | 971 | CMMSSY 2.3 |
| 8316 | 972 | CMMSSY 2.2 |
| 8712 | 973 | CMMSSY 2.2 |
| 8800 | 1037 | CMMSSY 2.2 |
| 8820 | 1038 | CMMSSY 2.2 |
| 9240 | 1039 | CMMSSY 2.2 |
| 9680 | 1040 | CMMSSY 2.2 |
| 9996 | 1041 | CMMSSY 2.3 |
| 10164 | 1042 | CMMSSY 2.2 |
| 10648 | 1043 | CMMSSY 2.2 |
| 10965 | 1089 | CMMSSY 2.3 |
| 20000 | 1105 | CMMSSY 2.3 |
| | Graph:
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