Best Known (58−41, 58, s)-Nets in Base 27
(58−41, 58, 96)-Net over F27 — Constructive and digital
Digital (17, 58, 96)-net over F27, using
- t-expansion [i] based on digital (11, 58, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(58−41, 58, 116)-Net in Base 27 — Constructive
(17, 58, 116)-net in base 27, using
- 2 times m-reduction [i] based on (17, 60, 116)-net in base 27, using
- base change [i] based on digital (2, 45, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 45, 116)-net over F81, using
(58−41, 58, 144)-Net over F27 — Digital
Digital (17, 58, 144)-net over F27, using
- t-expansion [i] based on digital (16, 58, 144)-net over F27, using
- net from sequence [i] based on digital (16, 143)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 16 and N(F) ≥ 144, using
- net from sequence [i] based on digital (16, 143)-sequence over F27, using
(58−41, 58, 3824)-Net in Base 27 — Upper bound on s
There is no (17, 58, 3825)-net in base 27, because
- 1 times m-reduction [i] would yield (17, 57, 3825)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 3883 695543 080024 728546 180058 502821 920989 801815 041248 289371 666119 872979 101201 824561 > 2757 [i]