**k** | **N** | **Source** |

7 | 7529536 | composition |

8 | 10000165 | composition |

17 | 16777214 | fuse symbols |

18 | 24137566 | fuse symbols |

19 | 36064754 | extend by one factor |

20 | 47045876 | fuse symbols |

23 | 67108853 | perfect hash family |

28 | 76658460 | Martirosyan-Tran van Trung |

34 | 80051208 | Martirosyan-Tran van Trung |

36 | 101600240 | Martirosyan-Tran van Trung |

37 | 133545244 | extend by one factor |

38 | 165490248 | extend by one factor |

39 | 167772131 | perfect hash family |

41 | 184549344 | perfect hash family |

42 | 218103770 | perfect hash family |

43 | 234880983 | perfect hash family |

46 | 235968072 | Martirosyan-Tran van Trung |

48 | 248554559 | Martirosyan-Tran van Trung |

85 | 251658196 | perfect hash family |

289 | 268435409 | Power 17^2 |

290 | 331205935 | extend by one factor |

291 | 404526819 | extend by one factor |

292 | 479530839 | extend by one factor |

513 | 536870817 | perfect hash family |

514 | 631496803 | extend by one factor |

515 | 726821669 | extend by one factor |

516 | 754974586 | perfect hash family |

517 | 850299452 | extend by one factor |

544 | 868528849 | Martirosyan-Tran van Trung |

576 | 904374213 | Martirosyan-Tran van Trung |

578 | 991141721 | Martirosyan-Tran van Trung |

580 | 1091892539 | Martirosyan-Tran van Trung |

582 | 1196775863 | Martirosyan-Tran van Trung |

964 | 1200768106 | linear hash family |

1026 | 1280819313 | Power 34^2 |

1027 | 1412766037 | extend by one factor |

1028 | 1544712761 | extend by one factor |

1029 | 1676659485 | extend by one factor |

1030 | 1808606209 | extend by one factor |

1056 | 1879047857 | perfect hash family |

1369 | 2003178646 | linear hash family |

1370 | 2137502654 | extend by one factor |

1425 | 2147483265 | perfect hash family |

1426 | 2281807273 | extend by one factor |

1428 | 2365587034 | perfect hash family |

1728 | 2415918673 | perfect hash family |

10000 | 2481587418 | Power 31^3 |