Best Known (145−82, 145, s)-Nets in Base 9
(145−82, 145, 106)-Net over F9 — Constructive and digital
Digital (63, 145, 106)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 46, 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 (17, 99, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- digital (5, 46, 32)-net over F9, using
(145−82, 145, 192)-Net over F9 — Digital
Digital (63, 145, 192)-net over F9, using
- t-expansion [i] based on digital (61, 145, 192)-net over F9, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
(145−82, 145, 4756)-Net in Base 9 — Upper bound on s
There is no (63, 145, 4757)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 2 325811 093211 191899 333080 610051 165482 006656 397126 633073 931251 446897 326968 243716 074036 928644 707273 399211 684906 490431 120599 443632 080079 380969 > 9145 [i]