Best Known (120−68, 120, s)-Nets in Base 9
(120−68, 120, 96)-Net over F9 — Constructive and digital
Digital (52, 120, 96)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 39, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (13, 81, 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 (5, 39, 32)-net over F9, using
(120−68, 120, 182)-Net over F9 — Digital
Digital (52, 120, 182)-net over F9, using
- t-expansion [i] based on digital (50, 120, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(120−68, 120, 3926)-Net in Base 9 — Upper bound on s
There is no (52, 120, 3927)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 3 240878 096323 174847 079220 493492 602214 962664 534272 615790 351779 250791 254701 571029 793021 154252 649953 905496 128074 520945 > 9120 [i]