Best Known (83−48, 83, s)-Nets in Base 27
(83−48, 83, 146)-Net over F27 — Constructive and digital
Digital (35, 83, 146)-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 (7, 55, 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, 28, 64)-net over F27, using
(83−48, 83, 224)-Net in Base 27 — Constructive
(35, 83, 224)-net in base 27, using
- 5 times m-reduction [i] based on (35, 88, 224)-net in base 27, using
- base change [i] based on digital (13, 66, 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, 66, 224)-net over F81, using
(83−48, 83, 230)-Net over F27 — Digital
Digital (35, 83, 230)-net over F27, using
(83−48, 83, 298)-Net in Base 27
(35, 83, 298)-net in base 27, using
- 9 times m-reduction [i] based on (35, 92, 298)-net in base 27, using
- base change [i] based on digital (12, 69, 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, 69, 298)-net over F81, using
(83−48, 83, 33601)-Net in Base 27 — Upper bound on s
There is no (35, 83, 33602)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 63572 639499 871371 796554 634736 170329 645793 581226 026118 991588 730920 052422 998864 328894 701893 369122 515925 542323 788711 578353 > 2783 [i]