Best Known (39−31, 39, s)-Nets in Base 9
(39−31, 39, 40)-Net over F9 — Constructive and digital
Digital (8, 39, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
(39−31, 39, 42)-Net over F9 — Digital
Digital (8, 39, 42)-net over F9, using
- net from sequence [i] based on digital (8, 41)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 42, using
(39−31, 39, 201)-Net in Base 9 — Upper bound on s
There is no (8, 39, 202)-net in base 9, because
- 1 times m-reduction [i] would yield (8, 38, 202)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1 935294 911088 992172 448031 202559 177329 > 938 [i]