Best Known (42, 96, s)-Nets in Base 9
(42, 96, 84)-Net over F9 — Constructive and digital
Digital (42, 96, 84)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 29, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (13, 67, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (2, 29, 20)-net over F9, using
(42, 96, 94)-Net in Base 9 — Constructive
(42, 96, 94)-net in base 9, using
- base change [i] based on digital (10, 64, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
(42, 96, 140)-Net over F9 — Digital
Digital (42, 96, 140)-net over F9, using
- t-expansion [i] based on digital (39, 96, 140)-net over F9, using
- net from sequence [i] based on digital (39, 139)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 39 and N(F) ≥ 140, using
- net from sequence [i] based on digital (39, 139)-sequence over F9, using
(42, 96, 3357)-Net in Base 9 — Upper bound on s
There is no (42, 96, 3358)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 40 512146 460184 438077 803951 615047 931690 885936 978982 775968 663677 606729 506524 436184 253665 776913 > 996 [i]