Best Known (41, 41+67, s)-Nets in Base 27
(41, 41+67, 128)-Net over F27 — Constructive and digital
Digital (41, 108, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 37, 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 (4, 71, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 37, 64)-net over F27, using
(41, 41+67, 224)-Net in Base 27 — Constructive
(41, 108, 224)-net in base 27, using
- t-expansion [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
(41, 41+67, 273)-Net over F27 — Digital
Digital (41, 108, 273)-net over F27, using
- t-expansion [i] based on digital (40, 108, 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
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
(41, 41+67, 298)-Net in Base 27
(41, 108, 298)-net in base 27, using
- t-expansion [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
(41, 41+67, 22137)-Net in Base 27 — Upper bound on s
There is no (41, 108, 22138)-net in base 27, because
- 1 times m-reduction [i] would yield (41, 107, 22138)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1432 764826 213154 003705 037285 593571 172425 201828 008418 893764 793063 994863 303357 434302 585055 355898 292375 922663 530873 469949 546632 220770 213561 575892 104629 969189 > 27107 [i]