Best Known (80−47, 80, s)-Nets in Base 27
(80−47, 80, 140)-Net over F27 — Constructive and digital
Digital (33, 80, 140)-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 (6, 53, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (4, 27, 64)-net over F27, using
(80−47, 80, 220)-Net over F27 — Digital
Digital (33, 80, 220)-net over F27, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 33 and N(F) ≥ 220, using
(80−47, 80, 224)-Net in Base 27 — Constructive
(33, 80, 224)-net in base 27, using
- base change [i] based on digital (13, 60, 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
(80−47, 80, 298)-Net in Base 27
(33, 80, 298)-net in base 27, using
- 4 times m-reduction [i] based on (33, 84, 298)-net in base 27, using
- base change [i] based on digital (12, 63, 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, 63, 298)-net over F81, using
(80−47, 80, 29904)-Net in Base 27 — Upper bound on s
There is no (33, 80, 29905)-net in base 27, because
- 1 times m-reduction [i] would yield (33, 79, 29905)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 119665 413183 333874 412762 336129 811834 416843 942336 690173 777311 232722 263506 872625 898024 053104 673329 749244 787537 077171 > 2779 [i]