Best Known (64−58, 64, s)-Nets in Base 16
(64−58, 64, 65)-Net over F16 — Constructive and digital
Digital (6, 64, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
(64−58, 64, 259)-Net in Base 16 — Upper bound on s
There is no (6, 64, 260)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1664, 260, S16, 58), but
- the linear programming bound shows that M ≥ 3 290218 640183 047376 007029 958582 538658 041212 526190 518014 704020 781060 570199 067378 412974 376729 969975 812205 327749 029256 433883 938816 / 28 100152 304190 433877 316878 061130 763004 425483 808791 > 1664 [i]