Best Known (6−5, 6, s)-Nets in Base 16
(6−5, 6, 24)-Net over F16 — Constructive and digital
Digital (1, 6, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
(6−5, 6, 25)-Net over F16 — Digital
Digital (1, 6, 25)-net over F16, using
- net from sequence [i] based on digital (1, 24)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 25, using
(6−5, 6, 93)-Net in Base 16 — Upper bound on s
There is no (1, 6, 94)-net in base 16, because
- 1 times m-reduction [i] would yield (1, 5, 94)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(165, 94, S16, 4), but
- the linear programming bound shows that M ≥ 2179 760128 / 2071 > 165 [i]
- extracting embedded orthogonal array [i] would yield OA(165, 94, S16, 4), but