Best Known (19, 59, s)-Nets in Base 27
(19, 59, 108)-Net over F27 — Constructive and digital
Digital (19, 59, 108)-net over F27, using
- t-expansion [i] based on digital (18, 59, 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
(19, 59, 148)-Net over F27 — Digital
Digital (19, 59, 148)-net over F27, using
- t-expansion [i] based on digital (18, 59, 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
(19, 59, 150)-Net in Base 27 — Constructive
(19, 59, 150)-net in base 27, using
- 1 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
(19, 59, 154)-Net in Base 27
(19, 59, 154)-net in base 27, using
- 1 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
(19, 59, 5321)-Net in Base 27 — Upper bound on s
There is no (19, 59, 5322)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2 828631 231429 696230 265603 907196 634897 364833 752591 922808 222383 795832 611753 375890 283081 > 2759 [i]