Best Known (40, 40+63, s)-Nets in Base 27
(40, 40+63, 132)-Net over F27 — Constructive and digital
Digital (40, 103, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 35, 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, 68, 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, 35, 64)-net over F27, using
(40, 40+63, 224)-Net in Base 27 — Constructive
(40, 103, 224)-net in base 27, using
- 5 times m-reduction [i] based on (40, 108, 224)-net in base 27, using
- base change [i] based on digital (13, 81, 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, 81, 224)-net over F81, using
(40, 40+63, 273)-Net over F27 — Digital
Digital (40, 103, 273)-net over F27, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 40 and N(F) ≥ 273, using
(40, 40+63, 298)-Net in Base 27
(40, 103, 298)-net in base 27, using
- t-expansion [i] based on (39, 103, 298)-net in base 27, using
- 5 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
- base change [i] based on digital (12, 81, 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, 81, 298)-net over F81, using
- 5 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
(40, 40+63, 24457)-Net in Base 27 — Upper bound on s
There is no (40, 103, 24458)-net in base 27, because
- 1 times m-reduction [i] would yield (40, 102, 24458)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 99 795306 565139 865941 009786 379439 071225 303892 583892 564637 840328 372466 529906 031984 194589 326950 371352 185456 936939 096014 664093 855843 359648 058479 022665 > 27102 [i]