Best Known (12, 12+18, s)-Nets in Base 9
(12, 12+18, 40)-Net over F9 — Constructive and digital
Digital (12, 30, 40)-net over F9, using
- t-expansion [i] based on digital (8, 30, 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
(12, 12+18, 48)-Net in Base 9 — Constructive
(12, 30, 48)-net in base 9, using
- base change [i] based on digital (2, 20, 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
(12, 12+18, 56)-Net over F9 — Digital
Digital (12, 30, 56)-net over F9, using
- net from sequence [i] based on digital (12, 55)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 12 and N(F) ≥ 56, using
(12, 12+18, 780)-Net in Base 9 — Upper bound on s
There is no (12, 30, 781)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 42405 123778 771244 733922 518697 > 930 [i]