Best Known (58−38, 58, s)-Nets in Base 27
(58−38, 58, 108)-Net over F27 — Constructive and digital
Digital (20, 58, 108)-net over F27, using
- t-expansion [i] based on digital (18, 58, 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
(58−38, 58, 148)-Net over F27 — Digital
Digital (20, 58, 148)-net over F27, using
- t-expansion [i] based on digital (18, 58, 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
(58−38, 58, 160)-Net in Base 27 — Constructive
(20, 58, 160)-net in base 27, using
- 2 times m-reduction [i] based on (20, 60, 160)-net in base 27, using
- base change [i] based on digital (5, 45, 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, 45, 160)-net over F81, using
(58−38, 58, 167)-Net in Base 27
(20, 58, 167)-net in base 27, using
- 2 times m-reduction [i] based on (20, 60, 167)-net in base 27, using
- base change [i] based on digital (5, 45, 167)-net over F81, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- base change [i] based on digital (5, 45, 167)-net over F81, using
(58−38, 58, 7129)-Net in Base 27 — Upper bound on s
There is no (20, 58, 7130)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 104556 329630 198109 015105 498415 007565 230946 706867 932810 692264 762010 646421 218926 832833 > 2758 [i]