Best Known (42−31, 42, s)-Nets in Base 9
(42−31, 42, 40)-Net over F9 — Constructive and digital
Digital (11, 42, 40)-net over F9, using
- t-expansion [i] based on digital (8, 42, 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
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
(42−31, 42, 55)-Net over F9 — Digital
Digital (11, 42, 55)-net over F9, using
- net from sequence [i] based on digital (11, 54)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 11 and N(F) ≥ 55, using
(42−31, 42, 316)-Net in Base 9 — Upper bound on s
There is no (11, 42, 317)-net in base 9, because
- 1 times m-reduction [i] would yield (11, 41, 317)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1330 919405 241871 242225 883412 260243 049817 > 941 [i]