| k | N | Source |
| 7 | 2985984 | composition |
| 8 | 3553567 | Add a symbol |
| 9 | 3876618 | Add a symbol |
| 10 | 4229037 | Add a symbol |
| 11 | 4613494 | Add a symbol |
| 14 | 4826807 | orthogonal array fuse |
| 15 | 8596595 | Add a factor |
| 16 | 12366383 | Add a factor |
| 17 | 16777208 | orthogonal array fuse fuse fuse fuse |
| 18 | 19307224 | perfect hash family4,18,14 |
| 20 | 22406866 | Martirosyan-Tran van Trung |
| 22 | 22791323 | Martirosyan-Tran van Trung |
| 24 | 23004636 | Martirosyan-Tran van Trung |
| 28 | 23061754 | Martirosyan-Tran van Trung |
| 29 | 32497774 | Add a factor |
| 30 | 42354082 | Add a factor |
| 32 | 53094866 | perfect hash family11,32,14 |
| 34 | 57921672 | perfect hash family12,34,14 |
| 37 | 62748478 | perfect hash family13,37,14 |
| 40 | 67575284 | perfect hash family14,40,14 |
| 43 | 72402090 | perfect hash family15,43,14 |
| 44 | 75930129 | Martirosyan-Tran van Trung |
| 46 | 76278707 | perfect hash family16,66,14T5 |
| 50 | 76631126 | perfect hash family16,65,13T3 |
| 55 | 77015583 | perfect hash family16,65,13T2 |
| 65 | 77228747 | perfect hash family16,65,13,c fuse |
| 66 | 77228896 | perfect hash family16,66,14 |
| 67 | 95208748 | Add a factor |
| 68 | 106189732 | perfect hash family22,68,14 |
| 69 | 111016319 | perfect hash family23,69,13,c fuse |
| 70 | 111016538 | perfect hash family23,70,14 |
| 71 | 115983794 | perfect hash family17,120,15S8 |
| 76 | 119753582 | perfect hash family17,120,15S7 |
| 81 | 123523370 | perfect hash family17,120,15S6 |
| 86 | 127293158 | perfect hash family17,120,15S5 |
| 92 | 131062946 | perfect hash family17,120,15S4 |
| 100 | 133775716 | Power 16^2T2S15 |
| 106 | 137545504 | Power 16^2S16 |
| 111 | 141315292 | Power 16^2S15 |
| 112 | 142372310 | perfect hash family17,120,15T1 |
| 117 | 145085080 | Power 16^2S14 |
| 120 | 146142098 | perfect hash family17,120,15 |
| 122 | 148854868 | Power 16^2S13 |
| 127 | 152624656 | Power 16^2S12 |
| 133 | 156394444 | Power 16^2S11 |
| 140 | 160164232 | Power 16^2S10 |
| 148 | 163934020 | Power 16^2S9 |
| 156 | 167703808 | Power 16^2S8 |
| 165 | 171473596 | Power 16^2S7 |
| 175 | 175243384 | Power 16^2S6 |
| 186 | 179013172 | Power 16^2S5 |
| 198 | 182782960 | Power 16^2S4 |
| 211 | 186552748 | Power 16^2S3 |
| 225 | 190322536 | Power 16^2T1T1 |
| 240 | 194092324 | Power 16^2T1 |
| 256 | 197862112 | Power 16^2 |
| 257 | 226035004 | Add a factor |
| 258 | 254207896 | Add a factor |
| 272 | 264024487 | Power 17^2T1 |
| 289 | 268435312 | Power 17^2 |
| 290 | 296608204 | Add a factor |
| 291 | 324781096 | Add a factor |
| 296 | 334302117 | Martirosyan-Tran van Trung |
| 312 | 338071905 | Martirosyan-Tran van Trung |
| 316 | 341841693 | Martirosyan-Tran van Trung |
| 330 | 342114115 | Martirosyan-Tran van Trung |
| 360 | 345271407 | Power N29^2T9S14 |
| 395 | 345655864 | Power N29^2T7S14 |
| 431 | 345869177 | Power N29^2T5S14 |
| 502 | 345926295 | Power N29^2S15 |
| 519 | 355362315 | Power N29^2S14 |
| 537 | 364798335 | Power N29^2S13 |
| 540 | 368333160 | Power 27^2T7 |
| 594 | 368717617 | Power 27^2T5 |
| 648 | 368930930 | Power 27^2T3 |
| 730 | 368988048 | Power 27^2+1 |
| 731 | 407849772 | Add a factor |
| 732 | 446711496 | Add a factor |
| 757 | 459158535 | Power N29^2S3 |
| 784 | 468594555 | Power N29^2T1T1 |
| 812 | 478030575 | Power N29^2T1 |
| 841 | 487466595 | Power N29^2 |
| 842 | 529293567 | Add a factor |
| 843 | 571120539 | Add a factor |
| 844 | 612947511 | Add a factor |
| 845 | 654774483 | Add a factor |
| 846 | 696601455 | Add a factor |
| 848 | 736325711 | Martirosyan-Tran van Trung |
| 862 | 736338031 | Martirosyan-Tran van Trung |
| 864 | 736395149 | Martirosyan-Tran van Trung |
| 884 | 736780413 | Martirosyan-Tran van Trung |
| 896 | 737271189 | Martirosyan-Tran van Trung |
| 900 | 739865847 | Martirosyan-Tran van Trung |
| 930 | 740149207 | Martirosyan-Tran van Trung |
| 936 | 740322975 | Martirosyan-Tran van Trung |
| 952 | 741833962 | Martirosyan-Tran van Trung |
| 954 | 741846282 | Martirosyan-Tran van Trung |
| 960 | 744077018 | Martirosyan-Tran van Trung |
| 988 | 744150938 | Martirosyan-Tran van Trung |
| 1004 | 745623266 | Martirosyan-Tran van Trung |
| 1032 | 755083926 | Martirosyan-Tran van Trung |
| 1038 | 755672740 | Martirosyan-Tran van Trung |
| 1074 | 765108760 | Martirosyan-Tran van Trung |
| 1080 | 769127119 | Martirosyan-Tran van Trung |
| 1106 | 769262639 | Martirosyan-Tran van Trung |
| 1140 | 769319757 | Martirosyan-Tran van Trung |
| 1152 | 769387484 | Martirosyan-Tran van Trung |
| 1190 | 769444602 | Martirosyan-Tran van Trung |
| 1200 | 769512395 | Martirosyan-Tran van Trung |
| 1204 | 770212089 | Martirosyan-Tran van Trung |
| 1228 | 772136649 | Martirosyan-Tran van Trung |
| 1248 | 780942537 | Martirosyan-Tran van Trung |
| 1264 | 782649121 | Martirosyan-Tran van Trung |
| 1272 | 782661441 | Martirosyan-Tran van Trung |
| 1292 | 782694595 | Martirosyan-Tran van Trung |
| 1296 | 782830115 | Martirosyan-Tran van Trung |
| 1322 | 782887233 | Martirosyan-Tran van Trung |
| 1332 | 792561009 | Martirosyan-Tran van Trung |
| 1352 | 793738637 | Martirosyan-Tran van Trung |
| 1360 | 794475890 | Martirosyan-Tran van Trung |
| 1420 | 801245015 | Martirosyan-Tran van Trung |
| 1460 | 806024231 | Martirosyan-Tran van Trung |
| 1461 | 847851203 | Add a factor |
| 1462 | 857657747 | Martirosyan-Tran van Trung |
| 1463 | 899484719 | Add a factor |
| 1464 | 902120528 | Martirosyan-Tran van Trung |
| 1466 | 915541012 | Martirosyan-Tran van Trung |
| 1470 | 920690452 | Martirosyan-Tran van Trung |
| 1472 | 930111476 | Martirosyan-Tran van Trung |
| 1508 | 930271636 | Martirosyan-Tran van Trung |
| 1514 | 930505287 | Martirosyan-Tran van Trung |
| 1516 | 939941307 | Martirosyan-Tran van Trung |
| 1534 | 942676795 | Martirosyan-Tran van Trung |
| 1536 | 962804539 | Martirosyan-Tran van Trung |
| 1538 | 966455747 | Martirosyan-Tran van Trung |
| 1540 | 968909363 | Martirosyan-Tran van Trung |
| 1552 | 980262467 | Martirosyan-Tran van Trung |
| 1560 | 980287107 | Martirosyan-Tran van Trung |
| 1568 | 980844290 | Martirosyan-Tran van Trung |
| 1600 | 990366550 | Martirosyan-Tran van Trung |
| 1624 | 990378870 | Martirosyan-Tran van Trung |
| 1660 | 999814890 | Martirosyan-Tran van Trung |
| 1664 | 1005627882 | Martirosyan-Tran van Trung |
| 1680 | 1005873270 | Martirosyan-Tran van Trung |
| 1682 | 1006107350 | Martirosyan-Tran van Trung |
| 1720 | 1008802440 | Power N43^2T3 |
| 1849 | 1013629246 | Power N43^2 |
| 1850 | 1055456218 | Add a factor |
| 1952 | 1057068563 | Power N61^2T29 |
| 2074 | 1061895369 | Power N61^2T27 |
| 2257 | 1066722175 | Power N61^2T24 |
| 2440 | 1071548981 | Power N61^2T21 |
| 2623 | 1076375787 | Power N61^2T18 |
| 2650 | 1077833691 | Power N53^2T3 |
| 2811 | 1078218148 | Power N53^2+2 |
| 3050 | 1080604823 | Power N61^2T11 |
| 3355 | 1080989280 | Power N61^2T6 |
| 3724 | 1081202444 | Power N61^2+3 |
| 3751 | 1117164234 | Power N67^2S12 |
| 3807 | 1135144086 | Power N67^2S11 |
| 3864 | 1153123938 | Power N67^2S10 |
| 3922 | 1171103790 | Power N67^2S9 |
| 3981 | 1189083642 | Power N67^2S8 |
| 4041 | 1207063494 | Power N67^2S7 |
| 4102 | 1225043346 | Power N67^2S6 |
| 4164 | 1243023198 | Power N67^2S5 |
| 4227 | 1261003050 | Power N67^2S4 |
| 5040 | 1275449236 | Power 31^3T17S30 |
| 5400 | 1279219024 | Power 31^3T16S30 |
| 5758 | 1282988812 | Power 31^3T15S30 |
| 6119 | 1287399637 | Power 31^3T14S30 |
| 6477 | 1289929653 | Power 31^3T13S30 |
| 7197 | 1293029295 | Power 31^3T11S30 |
| 7915 | 1293413752 | Power 31^3T9S30 |
| 8633 | 1293627065 | Power 31^3T7S30 |
| 10000 | 1293684183 | Power 31^3T3S30 |