Best Known (57−38, 57, s)-Nets in Base 27
(57−38, 57, 108)-Net over F27 — Constructive and digital
Digital (19, 57, 108)-net over F27, using
- t-expansion [i] based on digital (18, 57, 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
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
(57−38, 57, 148)-Net over F27 — Digital
Digital (19, 57, 148)-net over F27, using
- t-expansion [i] based on digital (18, 57, 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
- net from sequence [i] based on digital (18, 147)-sequence over F27, using
(57−38, 57, 150)-Net in Base 27 — Constructive
(19, 57, 150)-net in base 27, using
- 3 times m-reduction [i] based on (19, 60, 150)-net in base 27, using
- base change [i] based on digital (4, 45, 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, 45, 150)-net over F81, using
(57−38, 57, 154)-Net in Base 27
(19, 57, 154)-net in base 27, using
- 3 times m-reduction [i] based on (19, 60, 154)-net in base 27, using
- base change [i] based on digital (4, 45, 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, 45, 154)-net over F81, using
(57−38, 57, 5992)-Net in Base 27 — Upper bound on s
There is no (19, 57, 5993)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3872 776455 340541 066455 311137 210760 068476 616277 022223 878002 685412 654494 585835 714627 > 2757 [i]