Best Known (29, 29+48, s)-Nets in Base 128
(29, 29+48, 345)-Net over F128 — Constructive and digital
Digital (29, 77, 345)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 24, 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, 53, 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, 24, 129)-net over F128, using
(29, 29+48, 577)-Net over F128 — Digital
Digital (29, 77, 577)-net over F128, using
- t-expansion [i] based on digital (28, 77, 577)-net over F128, using
- net from sequence [i] based on digital (28, 576)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 28 and N(F) ≥ 577, using
- net from sequence [i] based on digital (28, 576)-sequence over F128, using
(29, 29+48, 444815)-Net in Base 128 — Upper bound on s
There is no (29, 77, 444816)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1 799646 213895 986294 923972 705220 801917 622135 697261 645691 170940 054077 809911 393911 307702 756117 576859 069703 968169 608766 227707 702784 539497 983332 406058 902539 288895 744488 > 12877 [i]