Best Known (43−31, 43, s)-Nets in Base 27
(43−31, 43, 96)-Net over F27 — Constructive and digital
Digital (12, 43, 96)-net over F27, using
- t-expansion [i] based on digital (11, 43, 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
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(43−31, 43, 100)-Net in Base 27 — Constructive
(12, 43, 100)-net in base 27, using
- 1 times m-reduction [i] based on (12, 44, 100)-net in base 27, using
- base change [i] based on digital (1, 33, 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
- base change [i] based on digital (1, 33, 100)-net over F81, using
(43−31, 43, 109)-Net over F27 — Digital
Digital (12, 43, 109)-net over F27, using
- net from sequence [i] based on digital (12, 108)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 12 and N(F) ≥ 109, using
(43−31, 43, 2507)-Net in Base 27 — Upper bound on s
There is no (12, 43, 2508)-net in base 27, because
- 1 times m-reduction [i] would yield (12, 42, 2508)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 311144 994895 872684 496503 402479 421484 276952 716264 188304 690865 > 2742 [i]