Best Known (9, 9+14, s)-Nets in Base 128
(9, 9+14, 300)-Net over F128 — Constructive and digital
Digital (9, 23, 300)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (1, 15, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (1, 8, 150)-net over F128, using
(9, 9+14, 301)-Net over F128 — Digital
Digital (9, 23, 301)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12823, 301, F128, 2, 14) (dual of [(301, 2), 579, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(1287, 129, F128, 2, 7) (dual of [(129, 2), 251, 8]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;251,128) [i]
- linear OOA(12816, 172, F128, 2, 14) (dual of [(172, 2), 328, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,329P) [i] based on function field F/F128 with g(F) = 2 and N(F) ≥ 172, using
- linear OOA(1287, 129, F128, 2, 7) (dual of [(129, 2), 251, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(9, 9+14, 386)-Net in Base 128 — Constructive
(9, 23, 386)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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
- (2, 16, 257)-net in base 128, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- digital (0, 7, 129)-net over F128, using
(9, 9+14, 223253)-Net in Base 128 — Upper bound on s
There is no (9, 23, 223254)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 2 923020 445821 915534 032741 645898 649211 568258 442696 > 12823 [i]