| k | N | Source |
| 12 | 1771561 | orthogonal array |
| 13 | 3367430 | extended OA (Colbourn) |
| 14 | 4826805 | orthogonal array fuse fuse |
| 15 | 7086240 | perfect hash family4,15,12 |
| 22 | 8213601 | double OA (Colbourn-Zhou) |
| 24 | 8373321 | double OA (Colbourn-Zhou) |
| 25 | 11593131 | Add a factor |
| 26 | 16263841 | Add a factor |
| 28 | 21665309 | Martirosyan-Tran van Trung |
| 29 | 24801840 | perfect hash family14,29,12 |
| 33 | 26573400 | perfect hash family15,33,12 |
| 36 | 28344960 | perfect hash family16,36,12 |
| 38 | 29256788 | Martirosyan-Tran van Trung |
| 40 | 29725124 | Martirosyan-Tran van Trung |
| 44 | 30076376 | Martirosyan-Tran van Trung |
| 46 | 30704432 | Martirosyan-Tran van Trung |
| 48 | 36235198 | Martirosyan-Tran van Trung |
| 49 | 40745880 | perfect hash family23,49,12 |
| 50 | 42517440 | perfect hash family24,50,12 |
| 52 | 44289000 | perfect hash family25,52,12 |
| 55 | 46060560 | perfect hash family26,55,12 |
| 59 | 47832120 | perfect hash family27,59,12 |
| 60 | 52282995 | perfect hash family16,65,13T1 |
| 65 | 53878864 | perfect hash family16,65,13 |
| 66 | 61478874 | Add a factor |
| 67 | 69078884 | Add a factor |
| 68 | 72528429 | Martirosyan-Tran van Trung |
| 70 | 72582549 | Martirosyan-Tran van Trung |
| 72 | 72831633 | Martirosyan-Tran van Trung |
| 76 | 76903321 | Martirosyan-Tran van Trung |
| 80 | 77443817 | Martirosyan-Tran van Trung |
| 88 | 77849189 | Martirosyan-Tran van Trung |
| 92 | 78549405 | Martirosyan-Tran van Trung |
| 96 | 85426231 | Martirosyan-Tran van Trung |
| 98 | 92853013 | Martirosyan-Tran van Trung |
| 100 | 95965593 | Martirosyan-Tran van Trung |
| 112 | 100936436 | Power CT16^2Arc(18):9 twos,0 ones |
| 113 | 105455306 | Power CT16^2Arc(18):7 twos,2 ones |
| 114 | 106582667 | Power CT16^2Arc(16):7 twos,1 ones |
| 116 | 107710028 | Power CT16^2Arc(14):7 twos,0 ones |
| 117 | 108842102 | Power CT16^2Arc(16):6 twos,2 ones |
| 120 | 109969463 | Power CT16^2Arc(14):6 twos,1 ones |
| 124 | 111096824 | Power CT16^2Arc(12):6 twos,0 ones |
| 125 | 112228898 | Power CT16^2Arc(14):5 twos,2 ones |
| 128 | 113024245 | Power CT16^2TD(4):3,2,2,2,2 |
| 130 | 113356259 | Power CT16^2Arc(12):5 twos,1 ones |
| 136 | 114483620 | Power CT16^2TD(4):2,2,2,2,2 |
| 137 | 115615694 | Power CT16^2Arc(12):4 twos,2 ones |
| 142 | 116411041 | Power CT16^2TD(4):3,2,2,2,0 |
| 144 | 116743055 | Power CT16^2TD(4):2,2,2,2,1 |
| 152 | 117870416 | Power CT16^2TD(4):2,2,2,2,0 |
| 153 | 119002490 | Power CT16^2TD(4):2,2,2,1,1 |
| 160 | 119797837 | Power CT16^2TD(2):2,2,3 |
| 162 | 120129851 | Power CT16^2TD(4):2,2,2,1,0 |
| 172 | 121257212 | Power CT16^2TD(2):2,2,2 |
| 173 | 122389286 | Power CT16^2TD(4):2,2,1,1,0 |
| 182 | 123184633 | Power CT16^2T3T2 |
| 184 | 123516647 | Power CT16^2TD(2):1,2,2 |
| 196 | 124644008 | Power CT16^2T2T2 |
| 228 | 124975560 | Power CT19^2T7 |
| 247 | 126571429 | Power CT19^2T6 |
| 253 | 127051920 | Power CT23^2Arc(2)T11 |
| 264 | 127211640 | Power CT23^2T11T1 |
| 276 | 127371360 | Power CT23^2T11 |
| 286 | 128807509 | Power CT23^2T10T1 |
| 299 | 128967229 | Power CT23^2T10 |
| 308 | 130266884 | Power CT23^2T9T1 |
| 322 | 130426604 | Power CT23^2T9 |
| 364 | 131417600 | Power CT19^2+3 |
| 373 | 132695360 | Power CT23^2Arc(8) |
| 389 | 132855080 | Power CT23^2Arc(7) |
| 406 | 133014800 | Power CT23^2Arc(6) |
| 424 | 133174520 | Power CT23^2Arc(5) |
| 443 | 133334240 | Power CT23^2Arc(4) |
| 463 | 133493960 | Power CT23^2Arc(3) |
| 484 | 133653680 | Power CT23^2T1T1 |
| 506 | 133813400 | Power CT23^2T1 |
| 530 | 133973120 | Power CT23^2+1 |
| 531 | 150345630 | Add a factor |
| 532 | 166718140 | Add a factor |
| 553 | 175830650 | Power CT25^2Arc(3) |
| 576 | 179050460 | Power CT25^2T1T1 |
| 600 | 182270270 | Power CT25^2T1 |
| 625 | 185490080 | Power CT25^2 |
| 626 | 203072590 | Add a factor |
| 627 | 220655100 | Add a factor |
| 628 | 238237610 | Add a factor |
| 629 | 255820120 | Add a factor |
| 630 | 273402630 | Add a factor |
| 632 | 278432154 | Martirosyan-Tran van Trung |
| 644 | 279252600 | Martirosyan-Tran van Trung |
| 648 | 280243596 | Martirosyan-Tran van Trung |
| 660 | 280517078 | Martirosyan-Tran van Trung |
| 672 | 280638078 | Martirosyan-Tran van Trung |
| 684 | 281239162 | Martirosyan-Tran van Trung |
| 696 | 281248182 | Martirosyan-Tran van Trung |
| 704 | 281521664 | Martirosyan-Tran van Trung |
| 708 | 281642664 | Martirosyan-Tran van Trung |
| 720 | 281651684 | Martirosyan-Tran van Trung |
| 726 | 281934186 | Martirosyan-Tran van Trung |
| 728 | 285482346 | Martirosyan-Tran van Trung |
| 746 | 286760106 | Martirosyan-Tran van Trung |
| 748 | 286919826 | Martirosyan-Tran van Trung |
| 750 | 287040826 | Martirosyan-Tran van Trung |
| 764 | 287324868 | Martirosyan-Tran van Trung |
| 768 | 287333888 | Martirosyan-Tran van Trung |
| 774 | 287415068 | Martirosyan-Tran van Trung |
| 778 | 287699110 | Martirosyan-Tran van Trung |
| 792 | 287858830 | Martirosyan-Tran van Trung |
| 796 | 292887832 | Martirosyan-Tran van Trung |
| 812 | 294963829 | Martirosyan-Tran van Trung |
| 824 | 295177669 | Martirosyan-Tran van Trung |
| 832 | 295475351 | Martirosyan-Tran van Trung |
| 836 | 295773033 | Martirosyan-Tran van Trung |
| 838 | 295894033 | Martirosyan-Tran van Trung |
| 840 | 308511913 | Martirosyan-Tran van Trung |
| 844 | 312732393 | Martirosyan-Tran van Trung |
| 848 | 312741413 | Martirosyan-Tran van Trung |
| 880 | 312901133 | Martirosyan-Tran van Trung |
| 886 | 313022133 | Martirosyan-Tran van Trung |
| 888 | 313181853 | Martirosyan-Tran van Trung |
| 896 | 313190873 | Martirosyan-Tran van Trung |
| 900 | 313226953 | Martirosyan-Tran van Trung |
| 912 | 313235973 | Martirosyan-Tran van Trung |
| 926 | 313254013 | Martirosyan-Tran van Trung |
| 928 | 313413733 | Martirosyan-Tran van Trung |
| 944 | 313422753 | Martirosyan-Tran van Trung |
| 968 | 313467853 | Martirosyan-Tran van Trung |
| 976 | 314112563 | Martirosyan-Tran van Trung |
| 1012 | 315064403 | Martirosyan-Tran van Trung |
| 1060 | 315224123 | Martirosyan-Tran van Trung |
| 1061 | 332806633 | Add a factor |
| 1062 | 338384733 | Martirosyan-Tran van Trung |
| 1063 | 355967243 | Add a factor |
| 1064 | 357282133 | Martirosyan-Tran van Trung |
| 1080 | 366394643 | Martirosyan-Tran van Trung |
| 1088 | 366421703 | Martirosyan-Tran van Trung |
| 1100 | 366475823 | Martirosyan-Tran van Trung |
| 1104 | 376882186 | Martirosyan-Tran van Trung |
| 1106 | 378201186 | Martirosyan-Tran van Trung |
| 1120 | 381420996 | Martirosyan-Tran van Trung |
| 1144 | 381439036 | Martirosyan-Tran van Trung |
| 1152 | 381520216 | Martirosyan-Tran van Trung |
| 1168 | 387244686 | Martirosyan-Tran van Trung |
| 1172 | 387289786 | Martirosyan-Tran van Trung |
| 1184 | 387298806 | Martirosyan-Tran van Trung |
| 1200 | 387307826 | Martirosyan-Tran van Trung |
| 1204 | 401699316 | Martirosyan-Tran van Trung |
| 1216 | 402409473 | Martirosyan-Tran van Trung |
| 1220 | 402477673 | Martirosyan-Tran van Trung |
| 1232 | 402486693 | Martirosyan-Tran van Trung |
| 1236 | 403120273 | Martirosyan-Tran van Trung |
| 1240 | 403129293 | Martirosyan-Tran van Trung |
| 1250 | 403138313 | Martirosyan-Tran van Trung |
| 1257 | 416512518 | Power N-CT41^2Arc(3)T8 |
| 1288 | 416863770 | Power N-CT41^2Arc(2)T8 |
| 1320 | 417215022 | Power N-CT41^2T8T1 |
| 1419 | 417566274 | Power N-CT43^2T10 |
| 1450 | 418961738 | Power N-CT41^2Arc(6) |
| 1486 | 419312990 | Power N-CT41^2Arc(5) |
| 1548 | 419337834 | Power N-CT43^2T7 |
| 1561 | 420015494 | Power N-CT41^2Arc(3) |
| 1634 | 420249662 | Power N-CT43^2T5 |
| 1720 | 420717998 | Power N-CT43^2T3 |
| 1850 | 421069250 | Power N-CT43^2+1 |
| 1852 | 429862034 | Power N-CT43^2+3 |
| 1853 | 453247264 | Add a factor |
| 1861 | 463046630 | Power N-CT47^2Arc(8) |
| 1901 | 468577396 | Power N-CT47^2Arc(7) |
| 1942 | 474108162 | Power N-CT47^2Arc(6) |
| 1984 | 479638928 | Power N-CT47^2Arc(5) |
| 2027 | 485169694 | Power N-CT47^2Arc(4) |
| 2071 | 490700460 | Power N-CT47^2Arc(3) |
| 2116 | 496231226 | Power N-CT47^2T1T1 |
| 2162 | 501761992 | Power N-CT47^2T1 |
| 2210 | 507292758 | Power N-CT47^2+1 |
| 2211 | 531955528 | Add a factor |
| 2212 | 556618298 | Add a factor |
| 2213 | 581281068 | Add a factor |
| 2214 | 605943838 | Add a factor |
| 2240 | 614733289 | Martirosyan-Tran van Trung |
| 2288 | 614769369 | Martirosyan-Tran van Trung |
| 2304 | 614931729 | Martirosyan-Tran van Trung |
| 2336 | 623160859 | Martirosyan-Tran van Trung |
| 2344 | 623251059 | Martirosyan-Tran van Trung |
| 2368 | 623269099 | Martirosyan-Tran van Trung |
| 2400 | 623287139 | Martirosyan-Tran van Trung |
| 2438 | 629491698 | Power N-CT53^2T7 |
| 2449 | 631479344 | Power N-CT53^2Arc(2)T5 |
| 2459 | 632446906 | Power N-CT53^2Arc(7) |
| 2496 | 633250904 | Power N-CT53^2T5T1 |
| 2506 | 634218466 | Power N-CT53^2Arc(6) |
| 2544 | 635022464 | Power N-CT53^2T5 |
| 2554 | 635990026 | Power N-CT53^2Arc(5) |
| 2603 | 637761586 | Power N-CT53^2Arc(4) |
| 2653 | 639533146 | Power N-CT53^2Arc(3) |
| 2704 | 641304706 | Power N-CT53^2T1T1 |
| 2756 | 643076266 | Power N-CT53^2T1 |
| 2811 | 644847826 | Power N-CT53^2+2 |
| 2832 | 658052744 | Power N-CT59^2T11 |
| 2838 | 662003687 | Martirosyan-Tran van Trung |
| 2891 | 662563426 | Power N-CT59^2T10 |
| 2900 | 663759555 | Martirosyan-Tran van Trung |
| 2904 | 664110807 | Martirosyan-Tran van Trung |
| 2950 | 664334986 | Power N-CT59^2T9 |
| 3068 | 666106546 | Power N-CT59^2T7 |
| 3245 | 667878106 | Power N-CT59^2T4 |
| 3481 | 669649666 | Power N-CT59^2 |
| 3482 | 698291576 | Add a factor |
| 3504 | 717568868 | Martirosyan-Tran van Trung |
| 3520 | 717601696 | Martirosyan-Tran van Trung |
| 3552 | 717722696 | Martirosyan-Tran van Trung |
| 3584 | 717731716 | Martirosyan-Tran van Trung |
| 3600 | 717767796 | Martirosyan-Tran van Trung |
| 3630 | 717776816 | Martirosyan-Tran van Trung |
| 3648 | 719528896 | Martirosyan-Tran van Trung |
| 3696 | 719546936 | Martirosyan-Tran van Trung |
| 3700 | 724362170 | Martirosyan-Tran van Trung |
| 3704 | 733154954 | Martirosyan-Tran van Trung |
| 3724 | 754304082 | Power N-CT61^2+3 |
| 3744 | 757567481 | Power CT31^3T19T18T7 |
| 4032 | 759026856 | Power CT31^3T19T17T7 |
| 4056 | 759163350 | Power CT31^3T18T18T7 |
| 4368 | 760622725 | Power CT31^3T18T17T7 |
| 4704 | 762082100 | Power CT31^3T17T17T7 |
| 5808 | 762253932 | Power CT31^3T19T9T9 |
| 6336 | 762413652 | Power CT31^3T19T9T7 |
| 6912 | 762573372 | Power CT31^3T19T7T7 |
| 7488 | 764169241 | Power CT31^3T18T7T7 |
| 8064 | 765628616 | Power CT31^3T17T7T7 |
| 8640 | 767888051 | Power CT31^3T16T7T7 |
| 10000 | 768695972 | Power CT31^3T10T9T9 |