Best Known (33, 33+48, s)-Nets in Base 27
(33, 33+48, 132)-Net over F27 — Constructive and digital
Digital (33, 81, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 28, 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, 53, 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, 28, 64)-net over F27, using
(33, 33+48, 172)-Net in Base 27 — Constructive
(33, 81, 172)-net in base 27, using
- 23 times m-reduction [i] based on (33, 104, 172)-net in base 27, using
- base change [i] based on digital (7, 78, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 78, 172)-net over F81, using
(33, 33+48, 220)-Net over F27 — Digital
Digital (33, 81, 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
(33, 33+48, 298)-Net in Base 27
(33, 81, 298)-net in base 27, using
- 3 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
(33, 33+48, 25528)-Net in Base 27 — Upper bound on s
There is no (33, 81, 25529)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 87 203979 636484 509492 076817 279980 892935 239951 843331 113633 124391 594677 758478 968873 075345 610491 049186 995603 566353 851297 > 2781 [i]