Best Known (55, 95, s)-Nets in Base 27
(55, 95, 248)-Net over F27 — Constructive and digital
Digital (55, 95, 248)-net over F27, using
- 1 times m-reduction [i] based on digital (55, 96, 248)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 20, 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 (7, 27, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (8, 49, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (7, 20, 82)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(55, 95, 398)-Net in Base 27 — Constructive
(55, 95, 398)-net in base 27, using
- (u, u+v)-construction [i] based on
- digital (0, 20, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- (35, 75, 370)-net in base 27, using
- 1 times m-reduction [i] based on (35, 76, 370)-net in base 27, using
- base change [i] based on digital (16, 57, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 57, 370)-net over F81, using
- 1 times m-reduction [i] based on (35, 76, 370)-net in base 27, using
- digital (0, 20, 28)-net over F27, using
(55, 95, 1835)-Net over F27 — Digital
Digital (55, 95, 1835)-net over F27, using
(55, 95, 2010520)-Net in Base 27 — Upper bound on s
There is no (55, 95, 2010521)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 9540 232999 381750 808129 227210 337503 336050 210512 038890 150416 675552 068427 362579 223927 842377 923648 190524 408860 794146 425143 108654 863749 241841 > 2795 [i]