Best Known (71−40, 71, s)-Nets in Base 27
(71−40, 71, 146)-Net over F27 — Constructive and digital
Digital (31, 71, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 24, 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, 47, 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, 24, 64)-net over F27, using
(71−40, 71, 224)-Net in Base 27 — Constructive
(31, 71, 224)-net in base 27, using
- 1 times m-reduction [i] based on (31, 72, 224)-net in base 27, using
- base change [i] based on digital (13, 54, 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, 54, 224)-net over F81, using
(71−40, 71, 236)-Net over F27 — Digital
Digital (31, 71, 236)-net over F27, using
(71−40, 71, 298)-Net in Base 27
(31, 71, 298)-net in base 27, using
- 5 times m-reduction [i] based on (31, 76, 298)-net in base 27, using
- base change [i] based on digital (12, 57, 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, 57, 298)-net over F81, using
(71−40, 71, 38508)-Net in Base 27 — Upper bound on s
There is no (31, 71, 38509)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 423548 342813 590947 098741 889236 465677 723586 182989 090805 673996 962880 555561 823404 130883 462677 392228 120433 > 2771 [i]