Best Known (47−30, 47, s)-Nets in Base 27
(47−30, 47, 96)-Net over F27 — Constructive and digital
Digital (17, 47, 96)-net over F27, using
- t-expansion [i] based on digital (11, 47, 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
(47−30, 47, 144)-Net over F27 — Digital
Digital (17, 47, 144)-net over F27, using
- t-expansion [i] based on digital (16, 47, 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
(47−30, 47, 160)-Net in Base 27 — Constructive
(17, 47, 160)-net in base 27, using
- 1 times m-reduction [i] based on (17, 48, 160)-net in base 27, using
- base change [i] based on digital (5, 36, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- base change [i] based on digital (5, 36, 160)-net over F81, using
(47−30, 47, 167)-Net in Base 27
(17, 47, 167)-net in base 27, using
- 1 times m-reduction [i] based on (17, 48, 167)-net in base 27, using
- base change [i] based on digital (5, 36, 167)-net over F81, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- base change [i] based on digital (5, 36, 167)-net over F81, using
(47−30, 47, 7538)-Net in Base 27 — Upper bound on s
There is no (17, 47, 7539)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 18 808281 216938 408983 963201 535305 995383 787971 180136 996170 755885 855083 > 2747 [i]