Best Known (41−26, 41, s)-Nets in Base 27
(41−26, 41, 96)-Net over F27 — Constructive and digital
Digital (15, 41, 96)-net over F27, using
- t-expansion [i] based on digital (11, 41, 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
(41−26, 41, 136)-Net over F27 — Digital
Digital (15, 41, 136)-net over F27, using
- t-expansion [i] based on digital (13, 41, 136)-net over F27, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
(41−26, 41, 150)-Net in Base 27 — Constructive
(15, 41, 150)-net in base 27, using
- 3 times m-reduction [i] based on (15, 44, 150)-net in base 27, using
- base change [i] based on digital (4, 33, 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, 33, 150)-net over F81, using
(41−26, 41, 154)-Net in Base 27
(15, 41, 154)-net in base 27, using
- 3 times m-reduction [i] based on (15, 44, 154)-net in base 27, using
- base change [i] based on digital (4, 33, 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, 33, 154)-net over F81, using
(41−26, 41, 7117)-Net in Base 27 — Upper bound on s
There is no (15, 41, 7118)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 48548 874117 478557 291850 379621 994787 333221 696836 029868 045557 > 2741 [i]