Best Known (27, 27+44, s)-Nets in Base 128
(27, 27+44, 345)-Net over F128 — Constructive and digital
Digital (27, 71, 345)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 22, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (5, 49, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- digital (0, 22, 129)-net over F128, using
(27, 27+44, 513)-Net over F128 — Digital
Digital (27, 71, 513)-net over F128, using
- t-expansion [i] based on digital (24, 71, 513)-net over F128, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
(27, 27+44, 450381)-Net in Base 128 — Upper bound on s
There is no (27, 71, 450382)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 409189 274565 316263 927532 464353 176321 734010 898188 149729 449693 075390 513943 867371 769503 637054 272060 744505 668043 005409 410976 929341 095269 667723 638045 039472 > 12871 [i]