| k | N | Source |
| 17 | 256 | orthogonal array |
| 18 | 286 | orthogonal array fuse |
| 19 | 288 | projection (Colbourn) |
| 20 | 345 | orthogonal array fuse fuse fuse postop NCK |
| 21 | 347 | projection (Colbourn) fuse fuse postop NCK |
| 22 | 348 | projection (Colbourn) fuse postop NCK |
| 23 | 351 | projection (Colbourn) postop NCK |
| 28 | 421 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 29 | 436 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 30 | 451 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 31 | 466 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 32 | 481 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 288 | 496 | CMMSSY 2.3 |
| 289 | 511 | CMMSSY 2.3 |
| 305 | 526 | CMMSSY 2.3 |
| 323 | 528 | CMMSSY 2.2 |
| 342 | 558 | CMMSSY 2.2 |
| 361 | 560 | CMMSSY 2.2 |
| 370 | 591 | CMMSSY 2.3 |
| 391 | 598 | CMMSSY 2.2 |
| 399 | 619 | CMMSSY 2.2 |
| 418 | 620 | CMMSSY 2.2 |
| 437 | 623 | CMMSSY 2.2 |
| 475 | 661 | CMMSSY 2.3 |
| 492 | 676 | CMMSSY 2.3 |
| 506 | 690 | CMMSSY 2.2 |
| 509 | 691 | CMMSSY 2.3 |
| 532 | 693 | CMMSSY 2.2 |
| 551 | 708 | CMMSSY 2.2 |
| 570 | 723 | CMMSSY 2.2 |
| 4880 | 736 | CMMSSY 2.3 |
| 4896 | 751 | CMMSSY 2.3 |
| 5168 | 766 | CMMSSY 2.3 |
| 5491 | 768 | CMMSSY 2.3 |
| 5814 | 798 | CMMSSY 2.2 |
| 6137 | 800 | CMMSSY 2.2 |
| 6156 | 828 | CMMSSY 2.2 |
| 6498 | 830 | CMMSSY 2.2 |
| 6859 | 832 | CMMSSY 2.2 |
| 7106 | 860 | CMMSSY 2.3 |
| 7429 | 863 | CMMSSY 2.3 |
| 7524 | 890 | CMMSSY 2.2 |
| 7581 | 891 | CMMSSY 2.2 |
| 7942 | 892 | CMMSSY 2.2 |
| 8303 | 895 | CMMSSY 2.2 |
| 8336 | 916 | CMMSSY 2.3 |
| 8468 | 926 | CMMSSY 2.2 |
| 8602 | 930 | CMMSSY 2.3 |
| 8624 | 931 | CMMSSY 2.3 |
| 9044 | 933 | CMMSSY 2.2 |
| 9367 | 948 | CMMSSY 2.2 |
| 9614 | 955 | CMMSSY 2.2 |
| 10051 | 958 | CMMSSY 2.2 |
| 10108 | 965 | CMMSSY 2.2 |
| 20000 | 976 | CMMSSY 2.2 |