Best Known (34, 34+47, s)-Nets in Base 27
(34, 34+47, 146)-Net over F27 — Constructive and digital
Digital (34, 81, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 27, 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 (7, 54, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 27, 64)-net over F27, using
(34, 34+47, 221)-Net over F27 — Digital
Digital (34, 81, 221)-net over F27, using
(34, 34+47, 224)-Net in Base 27 — Constructive
(34, 81, 224)-net in base 27, using
- 3 times m-reduction [i] based on (34, 84, 224)-net in base 27, using
- base change [i] based on digital (13, 63, 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, 63, 224)-net over F81, using
(34, 34+47, 298)-Net in Base 27
(34, 81, 298)-net in base 27, using
- 7 times m-reduction [i] based on (34, 88, 298)-net in base 27, using
- base change [i] based on digital (12, 66, 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, 66, 298)-net over F81, using
(34, 34+47, 34513)-Net in Base 27 — Upper bound on s
There is no (34, 81, 34514)-net in base 27, because
- 1 times m-reduction [i] would yield (34, 80, 34514)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 3 230152 647401 249150 200713 089961 757192 547702 306294 415384 204269 084439 510141 451827 467391 932330 605885 972986 385057 870137 > 2780 [i]