| k | N | Source |
| 8 | 343 | orthogonal array |
| 9 | 472 | simulated annealing (CKRS) |
| 10 | 479 | simulated annealing (CKRS) |
| 16 | 637 | Chateauneuf-Kreher doubling |
| 32 | 679 | Sherwood-Martirosyan-Colbourn |
| 56 | 931 | Colbourn-Martirosyan-Trung-Walker |
| 81 | 1015 | Sherwood-Martirosyan-Colbourn |
| 82 | 1309 | Add a factor |
| 150 | 1351 | Sherwood-Martirosyan-Colbourn |
| 198 | 1386 | Cyclotomy (Colbourn) |
| 212 | 1477 | Cyclotomy (Colbourn) |
| 224 | 1519 | Colbourn-Martirosyan-Trung-Walker |
| 256 | 1610 | Cohen-Colbourn-Ling |
| 392 | 1771 | Colbourn-Martirosyan-Trung-Walker |
| 441 | 1855 | Colbourn-Martirosyan-Trung-Walker |
| 448 | 1891 | Colbourn-Martirosyan-Trung-Walker |
| 455 | 1915 | Colbourn-Martirosyan-Trung-Walker |
| 553 | 1927 | Colbourn-Martirosyan-Trung-Walker |
| 560 | 1939 | Colbourn-Martirosyan-Trung-Walker |
| 567 | 1963 | Colbourn-Martirosyan-Trung-Walker |
| 648 | 2240 | Cohen-Colbourn-Ling |
| 693 | 2335 | Colbourn-Martirosyan-Trung-Walker |
| 700 | 2347 | Colbourn-Martirosyan-Trung-Walker |
| 721 | 2365 | Colbourn-Martirosyan-Trung-Walker |
| 763 | 2371 | Colbourn-Martirosyan-Trung-Walker |
| 784 | 2383 | Colbourn-Martirosyan-Trung-Walker |
| 798 | 2389 | Colbourn-Martirosyan-Trung-Walker |
| 833 | 2395 | Colbourn-Martirosyan-Trung-Walker |
| 847 | 2401 | Colbourn-Martirosyan-Trung-Walker |
| 889 | 2407 | Colbourn-Martirosyan-Trung-Walker |
| 896 | 2413 | Colbourn-Martirosyan-Trung-Walker |
| 945 | 2419 | Colbourn-Martirosyan-Trung-Walker |
| 1043 | 2431 | Colbourn-Martirosyan-Trung-Walker |
| 1050 | 2443 | Colbourn-Martirosyan-Trung-Walker |
| 1386 | 2478 | Colbourn-Martirosyan-Trung-Walker |
| 1484 | 2569 | Colbourn-Martirosyan-Trung-Walker |
| 1584 | 2611 | Cohen-Colbourn-Ling |
| 1792 | 2702 | Colbourn-Martirosyan-Trung-Walker |
| 2016 | 2786 | Cohen-Colbourn-Ling |
| 2048 | 2835 | Cohen-Colbourn-Ling |
| 2744 | 2863 | Colbourn-Martirosyan-Trung-Walker |
| 3087 | 2947 | Colbourn-Martirosyan-Trung-Walker |
| 3136 | 2983 | Colbourn-Martirosyan-Trung-Walker |
| 3185 | 3007 | Colbourn-Martirosyan-Trung-Walker |
| 3479 | 3019 | Colbourn-Martirosyan-Trung-Walker |
| 3528 | 3055 | Colbourn-Martirosyan-Trung-Walker |
| 3626 | 3079 | Colbourn-Martirosyan-Trung-Walker |
| 3871 | 3091 | Colbourn-Martirosyan-Trung-Walker |
| 3920 | 3103 | Colbourn-Martirosyan-Trung-Walker |
| 3969 | 3127 | Colbourn-Martirosyan-Trung-Walker |
| 4361 | 3404 | Colbourn-Martirosyan-Trung-Walker |
| 4480 | 3416 | Colbourn-Martirosyan-Trung-Walker |
| 4536 | 3440 | Colbourn-Martirosyan-Trung-Walker |
| 4802 | 3535 | Colbourn-Martirosyan-Trung-Walker |
| 4851 | 3571 | Colbourn-Martirosyan-Trung-Walker |
| 4900 | 3583 | Colbourn-Martirosyan-Trung-Walker |
| 5047 | 3601 | Colbourn-Martirosyan-Trung-Walker |
| 5341 | 3607 | Colbourn-Martirosyan-Trung-Walker |
| 5467 | 3619 | Colbourn-Martirosyan-Trung-Walker |
| 5488 | 3631 | Colbourn-Martirosyan-Trung-Walker |
| 5586 | 3637 | Colbourn-Martirosyan-Trung-Walker |
| 5600 | 3643 | Colbourn-Martirosyan-Trung-Walker |
| 6336 | 3661 | Cohen-Colbourn-Ling |
| 6370 | 3709 | Colbourn-Martirosyan-Trung-Walker |
| 6566 | 3715 | Colbourn-Martirosyan-Trung-Walker |
| 6615 | 3721 | Colbourn-Martirosyan-Trung-Walker |
| 7688 | 3732 | Power N31^3T23 |
| 8330 | 3810 | Colbourn-Martirosyan-Trung-Walker |
| 9702 | 3822 | Colbourn-Martirosyan-Trung-Walker |
| 10000 | 3913 | Colbourn-Martirosyan-Trung-Walker |