Best Known (47−29, 47, s)-Nets in Base 27
(47−29, 47, 108)-Net over F27 — Constructive and digital
Digital (18, 47, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
(47−29, 47, 148)-Net over F27 — Digital
Digital (18, 47, 148)-net over F27, using
- net from sequence [i] based on digital (18, 147)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 148, using
(47−29, 47, 160)-Net in Base 27 — Constructive
(18, 47, 160)-net in base 27, using
- 5 times m-reduction [i] based on (18, 52, 160)-net in base 27, using
- base change [i] based on digital (5, 39, 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, 39, 160)-net over F81, using
(47−29, 47, 190)-Net in Base 27
(18, 47, 190)-net in base 27, using
- 1 times m-reduction [i] based on (18, 48, 190)-net in base 27, using
- base change [i] based on digital (6, 36, 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, 36, 190)-net over F81, using
(47−29, 47, 11729)-Net in Base 27 — Upper bound on s
There is no (18, 47, 11730)-net in base 27, because
- 1 times m-reduction [i] would yield (18, 46, 11730)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 696686 490097 446053 634731 534443 289983 019345 847548 608383 194128 923309 > 2746 [i]