Best Known (9−7, 9, s)-Nets in Base 8
(9−7, 9, 17)-Net over F8 — Constructive and digital
Digital (2, 9, 17)-net over F8, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
(9−7, 9, 18)-Net over F8 — Digital
Digital (2, 9, 18)-net over F8, using
- net from sequence [i] based on digital (2, 17)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 18, using
(9−7, 9, 65)-Net in Base 8 — Upper bound on s
There is no (2, 9, 66)-net in base 8, because
- 1 times m-reduction [i] would yield (2, 8, 66)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 17 516192 > 88 [i]
- extracting embedded orthogonal array [i] would yield OA(88, 66, S8, 6), but
- the linear programming bound shows that M ≥ 904771 551232 / 52139 > 88 [i]