Best Known (45−24, 45, s)-Nets in Base 9
(45−24, 45, 74)-Net over F9 — Constructive and digital
Digital (21, 45, 74)-net over F9, using
- t-expansion [i] based on digital (17, 45, 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
(45−24, 45, 76)-Net in Base 9 — Constructive
(21, 45, 76)-net in base 9, using
- base change [i] based on digital (6, 30, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
(45−24, 45, 88)-Net over F9 — Digital
Digital (21, 45, 88)-net over F9, using
- net from sequence [i] based on digital (21, 87)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 21 and N(F) ≥ 88, using
(45−24, 45, 2497)-Net in Base 9 — Upper bound on s
There is no (21, 45, 2498)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 8 758364 153251 296828 809608 278986 433685 396033 > 945 [i]