Best Known (40−35, 40, s)-Nets in Base 16
(40−35, 40, 49)-Net over F16 — Constructive and digital
Digital (5, 40, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
(40−35, 40, 262)-Net in Base 16 — Upper bound on s
There is no (5, 40, 263)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1640, 263, S16, 35), but
- the linear programming bound shows that M ≥ 1 028582 672548 795249 215524 568982 893466 019859 247220 759568 697178 089495 734339 170294 575247 917056 / 668632 979262 103744 476567 954302 294855 148361 > 1640 [i]