Best Known (18, 55, s)-Nets in Base 27
(18, 55, 108)-Net over F27 — Constructive and digital
Digital (18, 55, 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
(18, 55, 148)-Net over F27 — Digital
Digital (18, 55, 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
(18, 55, 150)-Net in Base 27 — Constructive
(18, 55, 150)-net in base 27, using
- 1 times m-reduction [i] based on (18, 56, 150)-net in base 27, using
- base change [i] based on digital (4, 42, 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, 42, 150)-net over F81, using
(18, 55, 154)-Net in Base 27
(18, 55, 154)-net in base 27, using
- 1 times m-reduction [i] based on (18, 56, 154)-net in base 27, using
- base change [i] based on digital (4, 42, 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, 42, 154)-net over F81, using
(18, 55, 5708)-Net in Base 27 — Upper bound on s
There is no (18, 55, 5709)-net in base 27, because
- 1 times m-reduction [i] would yield (18, 54, 5709)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 196712 605800 702173 968221 099217 631466 688425 314010 417319 310044 145128 114595 300145 > 2754 [i]