Best Known (38, 38+58, s)-Nets in Base 27
(38, 38+58, 132)-Net over F27 — Constructive and digital
Digital (38, 96, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 33, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (5, 63, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (4, 33, 64)-net over F27, using
(38, 38+58, 224)-Net in Base 27 — Constructive
(38, 96, 224)-net in base 27, using
- 4 times m-reduction [i] based on (38, 100, 224)-net in base 27, using
- base change [i] based on digital (13, 75, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 75, 224)-net over F81, using
(38, 38+58, 244)-Net over F27 — Digital
Digital (38, 96, 244)-net over F27, using
- t-expansion [i] based on digital (36, 96, 244)-net over F27, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 36 and N(F) ≥ 244, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
(38, 38+58, 298)-Net in Base 27
(38, 96, 298)-net in base 27, using
- 8 times m-reduction [i] based on (38, 104, 298)-net in base 27, using
- base change [i] based on digital (12, 78, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 78, 298)-net over F81, using
(38, 38+58, 24557)-Net in Base 27 — Upper bound on s
There is no (38, 96, 24558)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 257652 037005 793606 734984 986892 626242 608757 694401 651900 731249 393894 074018 204747 897133 137367 670695 679331 277098 912174 292087 837159 777801 661461 > 2796 [i]