Best Known (49−32, 49, s)-Nets in Base 27
(49−32, 49, 96)-Net over F27 — Constructive and digital
Digital (17, 49, 96)-net over F27, using
- t-expansion [i] based on digital (11, 49, 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
(49−32, 49, 144)-Net over F27 — Digital
Digital (17, 49, 144)-net over F27, using
- t-expansion [i] based on digital (16, 49, 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
(49−32, 49, 150)-Net in Base 27 — Constructive
(17, 49, 150)-net in base 27, using
- 3 times m-reduction [i] based on (17, 52, 150)-net in base 27, using
- base change [i] based on digital (4, 39, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- base change [i] based on digital (4, 39, 150)-net over F81, using
(49−32, 49, 154)-Net in Base 27
(17, 49, 154)-net in base 27, using
- 3 times m-reduction [i] based on (17, 52, 154)-net in base 27, using
- base change [i] based on digital (4, 39, 154)-net over F81, using
- net from sequence [i] based on digital (4, 153)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 154, using
- net from sequence [i] based on digital (4, 153)-sequence over F81, using
- base change [i] based on digital (4, 39, 154)-net over F81, using
(49−32, 49, 6317)-Net in Base 27 — Upper bound on s
There is no (17, 49, 6318)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 13713 396724 662216 811952 372579 691649 031982 290452 415522 089608 751994 882977 > 2749 [i]