Best Known (45, 45+52, s)-Nets in Base 9
(45, 45+52, 98)-Net over F9 — Constructive and digital
Digital (45, 97, 98)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 32, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- digital (13, 65, 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 (6, 32, 34)-net over F9, using
(45, 45+52, 147)-Net over F9 — Digital
Digital (45, 97, 147)-net over F9, using
- t-expansion [i] based on digital (43, 97, 147)-net over F9, using
- net from sequence [i] based on digital (43, 146)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 43 and N(F) ≥ 147, using
- net from sequence [i] based on digital (43, 146)-sequence over F9, using
(45, 45+52, 4773)-Net in Base 9 — Upper bound on s
There is no (45, 97, 4774)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 365 441902 135353 072552 747830 976043 096350 576166 622345 575027 813465 313966 112274 289749 992263 410977 > 997 [i]