Best Known (65−59, 65, s)-Nets in Base 16
(65−59, 65, 65)-Net over F16 — Constructive and digital
Digital (6, 65, 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
(65−59, 65, 258)-Net in Base 16 — Upper bound on s
There is no (6, 65, 259)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1665, 259, S16, 59), but
- the linear programming bound shows that M ≥ 56 276572 650645 541349 006166 971411 454658 492486 845808 946236 493211 500346 203572 796245 849632 672306 232020 495859 526278 030448 483343 794176 / 30 003791 214490 297290 429534 847599 708209 937909 006961 > 1665 [i]