Best Known (21−12, 21, s)-Nets in Base 9
(21−12, 21, 40)-Net over F9 — Constructive and digital
Digital (9, 21, 40)-net over F9, using
- t-expansion [i] based on digital (8, 21, 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
(21−12, 21, 48)-Net in Base 9 — Constructive
(9, 21, 48)-net in base 9, using
- base change [i] based on digital (2, 14, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
(21−12, 21, 48)-Net over F9 — Digital
Digital (9, 21, 48)-net over F9, using
- net from sequence [i] based on digital (9, 47)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 9 and N(F) ≥ 48, using
(21−12, 21, 815)-Net in Base 9 — Upper bound on s
There is no (9, 21, 816)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 110 075911 657180 050177 > 921 [i]