Best Known (12, 36, s)-Nets in Base 27
(12, 36, 96)-Net over F27 — Constructive and digital
Digital (12, 36, 96)-net over F27, using
- t-expansion [i] based on digital (11, 36, 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
(12, 36, 109)-Net over F27 — Digital
Digital (12, 36, 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
(12, 36, 116)-Net in Base 27 — Constructive
(12, 36, 116)-net in base 27, using
- 4 times m-reduction [i] based on (12, 40, 116)-net in base 27, using
- base change [i] based on digital (2, 30, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 30, 116)-net over F81, using
(12, 36, 136)-Net in Base 27
(12, 36, 136)-net in base 27, using
- base change [i] based on digital (3, 27, 136)-net over F81, using
- net from sequence [i] based on digital (3, 135)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 3 and N(F) ≥ 136, using
- net from sequence [i] based on digital (3, 135)-sequence over F81, using
(12, 36, 3997)-Net in Base 27 — Upper bound on s
There is no (12, 36, 3998)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3382 354964 376815 361470 322618 840365 479928 325872 811993 > 2736 [i]