Best Known (41, 41+61, s)-Nets in Base 27
(41, 41+61, 146)-Net over F27 — Constructive and digital
Digital (41, 102, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 34, 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, 68, 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, 34, 64)-net over F27, using
(41, 41+61, 224)-Net in Base 27 — Constructive
(41, 102, 224)-net in base 27, using
- t-expansion [i] based on (40, 102, 224)-net in base 27, using
- 6 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
- 6 times m-reduction [i] based on (40, 108, 224)-net in base 27, using
(41, 41+61, 273)-Net over F27 — Digital
Digital (41, 102, 273)-net over F27, using
- t-expansion [i] based on digital (40, 102, 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+61, 298)-Net in Base 27
(41, 102, 298)-net in base 27, using
- t-expansion [i] based on (39, 102, 298)-net in base 27, using
- 6 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
- 6 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
(41, 41+61, 30515)-Net in Base 27 — Upper bound on s
There is no (41, 102, 30516)-net in base 27, because
- 1 times m-reduction [i] would yield (41, 101, 30516)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 3 698703 302649 492937 077574 891012 282254 743146 787026 227197 555073 590069 873178 131037 520262 175581 777811 983995 099901 082740 364804 905644 628264 708579 162105 > 27101 [i]