| k | N | Source |
| 7 | 7529536 | composition |
| 8 | 8732479 | Add a symbol |
| 9 | 9404208 | Add a symbol |
| 10 | 10127608 | Add a symbol |
| 11 | 10906654 | Add a symbol |
| 12 | 11745627 | Add a symbol |
| 13 | 12649136 | Add a symbol |
| 14 | 13622146 | Add a symbol |
| 17 | 16777212 | orthogonal array fuse fuse |
| 18 | 24137563 | orthogonal array fuse fuse fuse |
| 19 | 36042001 | Add a factor |
| 20 | 47045871 | orthogonal array fuse fuse fuse fuse fuse |
| 22 | 61976918 | Martirosyan-Tran van Trung |
| 24 | 66438200 | Martirosyan-Tran van Trung |
| 26 | 69105148 | Martirosyan-Tran van Trung |
| 28 | 71181204 | Martirosyan-Tran van Trung |
| 30 | 77886048 | Martirosyan-Tran van Trung |
| 32 | 78280197 | Martirosyan-Tran van Trung |
| 34 | 78472564 | Martirosyan-Tran van Trung |
| 36 | 99799254 | Martirosyan-Tran van Trung |
| 37 | 131460156 | Add a factor |
| 38 | 161954578 | Martirosyan-Tran van Trung |
| 39 | 167772110 | perfect hash family10,39,17 |
| 40 | 180693872 | Martirosyan-Tran van Trung |
| 44 | 184549321 | perfect hash family11,44,17 |
| 45 | 197868615 | perfect hash family16,65,13S5 |
| 48 | 198772124 | perfect hash family16,65,13S4 |
| 52 | 199675633 | perfect hash family16,65,13S3 |
| 56 | 200579142 | perfect hash family16,65,13S2 |
| 60 | 201482651 | perfect hash family16,65,13T1 |
| 65 | 202386160 | perfect hash family16,65,13 |
| 66 | 217954320 | perfect hash family16,66,14 |
| 112 | 240039782 | Power CT16^2Arc(18):9 twos,0 ones |
| 116 | 246349914 | Power CT16^2Arc(14):7 twos,0 ones |
| 124 | 249504980 | Power CT16^2Arc(12):6 twos,0 ones |
| 128 | 251687036 | Power CT16^2TD(4):3,2,2,2,2 |
| 136 | 252660046 | Power CT16^2TD(4):2,2,2,2,2 |
| 142 | 254842102 | Power CT16^2TD(4):3,2,2,2,0 |
| 152 | 255815112 | Power CT16^2TD(4):2,2,2,2,0 |
| 160 | 257997168 | Power CT16^2TD(2):2,2,3 |
| 172 | 258970178 | Power CT16^2TD(2):2,2,2 |
| 182 | 261152234 | Power CT16^2T3T2 |
| 196 | 262125244 | Power CT16^2T2T2 |
| 204 | 263403791 | Power CT17^2T5 |
| 221 | 264307300 | Power CT17^2T4 |
| 238 | 265280310 | Power CT17^2T3 |
| 256 | 268435212 | perfect hash family16,256,16,c fuse fuse |
| 289 | 268435376 | Power CT17^2 |
| 290 | 332673186 | Add a factor |
| 291 | 398607236 | Add a factor |
| 292 | 467763960 | Add a factor |
| 293 | 520093541 | perfect hash family31,293,17 |
| 320 | 530221148 | perfect hash family32,512,16T6 |
| 352 | 531000194 | perfect hash family32,512,16T5 |
| 384 | 531839167 | perfect hash family32,512,16T4 |
| 416 | 532742676 | perfect hash family32,512,16T3 |
| 448 | 533715686 | perfect hash family32,512,16T2 |
| 512 | 536870412 | perfect hash family32,512,16,c fuse fuse |
| 513 | 536870752 | perfect hash family32,513,17 |
| 514 | 630770376 | Add a factor |
| 515 | 725834982 | Add a factor |
| 516 | 754974495 | perfect hash family45,516,17 |
| 517 | 850039101 | Add a factor |
| 544 | 858958921 | Martirosyan-Tran van Trung |
| 576 | 886438073 | Martirosyan-Tran van Trung |
| 578 | 900492105 | Martirosyan-Tran van Trung |
| 579 | 1002089055 | Add a factor |
| 580 | 1011069967 | Martirosyan-Tran van Trung |
| 582 | 1097692786 | Martirosyan-Tran van Trung |
| 596 | 1101242265 | Power N-CT29^2Arc(10) |
| 600 | 1103015404 | Power CT25^2T1 |
| 626 | 1105682352 | Power CT25^2+1 |
| 637 | 1114651953 | Power N-CT29^2Arc(8) |
| 659 | 1121356797 | Power N-CT29^2Arc(7) |
| 682 | 1128061641 | Power N-CT29^2Arc(6) |
| 706 | 1134766485 | Power N-CT29^2Arc(5) |
| 730 | 1138899248 | Power CT27^2+1 |
| 731 | 1141471329 | Power N-CT29^2Arc(4) |
| 757 | 1148176173 | Power N-CT29^2Arc(3) |
| 784 | 1154881017 | Power N-CT29^2T1T1 |
| 812 | 1161585861 | Power N-CT29^2T1 |
| 813 | 1166315649 | Power N-CT31^2Arc(2)T3 |
| 840 | 1166709798 | Power N-CT31^2T3T1 |
| 868 | 1167103947 | Power N-CT31^2T3 |
| 871 | 1173020493 | Power N-CT31^2Arc(3) |
| 900 | 1173414642 | Power N-CT31^2T1T1 |
| 930 | 1173808791 | Power N-CT31^2T1 |
| 962 | 1174202940 | Power N-CT31^2+1 |
| 964 | 1177088445 | Power N-CT31^2+3 |
| 1024 | 1252483136 | Power CT32^2 |
| 1026 | 1255561008 | Power CT32^2+2 |
| 1027 | 1377994774 | Add a factor |
| 1028 | 1500428540 | Add a factor |
| 1029 | 1622862306 | Add a factor |
| 1044 | 1655293305 | Power N-CT37^2Arc(10) |
| 1072 | 1686954207 | Power N-CT37^2Arc(9) |
| 1101 | 1718615109 | Power N-CT37^2Arc(8) |
| 1131 | 1750276011 | Power N-CT37^2Arc(7) |
| 1162 | 1781936913 | Power N-CT37^2Arc(6) |
| 1194 | 1813597815 | Power N-CT37^2Arc(5) |
| 1227 | 1845258717 | Power N-CT37^2Arc(4) |
| 1261 | 1876919619 | Power N-CT37^2Arc(3) |
| 1296 | 1908580521 | Power N-CT37^2T1T1 |
| 1332 | 1940241423 | Power N-CT37^2T1 |
| 1369 | 1971902325 | Power N-CT37^2 |
| 1370 | 2098220517 | Add a factor |
| 1425 | 2147483008 | perfect hash family128,1425,17 |
| 1452 | 2225404420 | Power CT31^3T20T20T19 |
| 1584 | 2226243393 | Power CT31^3T20T19T19 |
| 1728 | 2227082366 | Power CT31^3T19T19T19 |
| 1872 | 2227985875 | Power CT31^3T19T19T18 |
| 2028 | 2228889384 | Power CT31^3T19T18T18 |
| 2197 | 2229792893 | Power CT31^3T18T18T18 |
| 2366 | 2230765903 | Power CT31^3T18T18T17 |
| 2548 | 2231738913 | Power CT31^3T18T17T17 |
| 2744 | 2232711923 | Power CT31^3T17T17T17 |
| 2873 | 2233920969 | Power CT31^3T18T18T14 |
| 3094 | 2234893979 | Power CT31^3T18T17T14 |
| 3332 | 2235866989 | Power CT31^3T17T17T14 |
| 3468 | 2237145536 | Power CT31^3T19T14T14 |
| 3757 | 2238049045 | Power CT31^3T18T14T14 |
| 4046 | 2239022055 | Power CT31^3T17T14T14 |
| 4913 | 2242177121 | Power CT31^3T14T14T14 |
| 5202 | 2249537472 | Power CT31^3T14T14T13 |
| 5508 | 2256897823 | Power CT31^3T14T13T13 |
| 5832 | 2264258174 | Power CT31^3T13T13T13 |
| 6156 | 2276162612 | Power CT31^3T13T13T12 |
| 6480 | 2287166482 | Power CT31^3T13T13T11 |
| 6498 | 2288067050 | Power CT31^3T13T12T12 |
| 6936 | 2291838109 | Power CT31^3T14T14T7 |
| 7514 | 2294505057 | Power CT31^3T14T14T5 |
| 8092 | 2296581113 | Power CT31^3T14T14T3 |
| 8670 | 2303285957 | Power CT31^3T14T14T1 |
| 9248 | 2303680106 | Power CT32^3T15T15 |
| 9792 | 2311040457 | Power CT32^3T15T14 |
| 10000 | 2318400808 | Power CT31^3T13T13 |