Best Known (40−29, 40, s)-Nets in Base 27
(40−29, 40, 96)-Net over F27 — Constructive and digital
Digital (11, 40, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
(40−29, 40, 100)-Net in Base 27 — Constructive
(11, 40, 100)-net in base 27, using
- base change [i] based on digital (1, 30, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
(40−29, 40, 100)-Net over F27 — Digital
Digital (11, 40, 100)-net over F27, using
- net from sequence [i] based on digital (11, 99)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 100, using
(40−29, 40, 2251)-Net in Base 27 — Upper bound on s
There is no (11, 40, 2252)-net in base 27, because
- 1 times m-reduction [i] would yield (11, 39, 2252)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 66 701449 034107 793112 686843 838681 077150 018171 883943 807497 > 2739 [i]