Best Known (40−23, 40, s)-Nets in Base 27
(40−23, 40, 112)-Net over F27 — Constructive and digital
Digital (17, 40, 112)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 13, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- digital (4, 27, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (2, 13, 48)-net over F27, using
(40−23, 40, 144)-Net over F27 — Digital
Digital (17, 40, 144)-net over F27, using
- t-expansion [i] based on digital (16, 40, 144)-net over F27, using
- net from sequence [i] based on digital (16, 143)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 16 and N(F) ≥ 144, using
- net from sequence [i] based on digital (16, 143)-sequence over F27, using
(40−23, 40, 172)-Net in Base 27 — Constructive
(17, 40, 172)-net in base 27, using
- base change [i] based on digital (7, 30, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(40−23, 40, 190)-Net in Base 27
(17, 40, 190)-net in base 27, using
- 4 times m-reduction [i] based on (17, 44, 190)-net in base 27, using
- base change [i] based on digital (6, 33, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- base change [i] based on digital (6, 33, 190)-net over F81, using
(40−23, 40, 22426)-Net in Base 27 — Upper bound on s
There is no (17, 40, 22427)-net in base 27, because
- 1 times m-reduction [i] would yield (17, 39, 22427)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 66 556289 229868 052975 015949 222799 697758 941744 307875 520467 > 2739 [i]