Best Known (40, 40+57, s)-Nets in Base 27
(40, 40+57, 152)-Net over F27 — Constructive and digital
Digital (40, 97, 152)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 34, 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 (6, 63, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 34, 76)-net over F27, using
(40, 40+57, 224)-Net in Base 27 — Constructive
(40, 97, 224)-net in base 27, using
- 11 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+57, 273)-Net over F27 — Digital
Digital (40, 97, 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+57, 298)-Net in Base 27
(40, 97, 298)-net in base 27, using
- t-expansion [i] based on (39, 97, 298)-net in base 27, using
- 11 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
- 11 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
(40, 40+57, 35106)-Net in Base 27 — Upper bound on s
There is no (40, 97, 35107)-net in base 27, because
- 1 times m-reduction [i] would yield (40, 96, 35107)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 257741 675806 404035 734391 103020 921918 095374 182685 707125 705192 304558 383256 204632 169660 561458 451666 391494 358350 454025 512899 306651 852826 377865 > 2796 [i]