Best Known (19, 19+26, s)-Nets in Base 27
(19, 19+26, 112)-Net over F27 — Constructive and digital
Digital (19, 45, 112)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 15, 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, 30, 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, 15, 48)-net over F27, using
(19, 19+26, 150)-Net over F27 — Digital
Digital (19, 45, 150)-net over F27, using
(19, 19+26, 172)-Net in Base 27 — Constructive
(19, 45, 172)-net in base 27, using
- 3 times m-reduction [i] based on (19, 48, 172)-net in base 27, using
- base change [i] based on digital (7, 36, 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
- base change [i] based on digital (7, 36, 172)-net over F81, using
(19, 19+26, 190)-Net in Base 27
(19, 45, 190)-net in base 27, using
- 7 times m-reduction [i] based on (19, 52, 190)-net in base 27, using
- base change [i] based on digital (6, 39, 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, 39, 190)-net over F81, using
(19, 19+26, 19634)-Net in Base 27 — Upper bound on s
There is no (19, 45, 19635)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 25801 415126 271685 145239 989136 817542 369030 215342 873200 840904 328503 > 2745 [i]