Best Known (47−28, 47, s)-Nets in Base 128
(47−28, 47, 345)-Net over F128 — Constructive and digital
Digital (19, 47, 345)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 14, 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, 33, 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, 14, 129)-net over F128, using
(47−28, 47, 407)-Net in Base 128 — Constructive
(19, 47, 407)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (1, 15, 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
- (4, 32, 257)-net in base 128, using
- base change [i] based on digital (0, 28, 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, 28, 257)-net over F256, using
- digital (1, 15, 150)-net over F128, using
(47−28, 47, 425)-Net over F128 — Digital
Digital (19, 47, 425)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12847, 425, F128, 28) (dual of [425, 378, 29]-code), using
- 35 step Varšamov–Edel lengthening with (ri) = (3, 6 times 0, 1, 27 times 0) [i] based on linear OA(12843, 386, F128, 28) (dual of [386, 343, 29]-code), using
- extended algebraic-geometric code AGe(F,357P) [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- 35 step Varšamov–Edel lengthening with (ri) = (3, 6 times 0, 1, 27 times 0) [i] based on linear OA(12843, 386, F128, 28) (dual of [386, 343, 29]-code), using
(47−28, 47, 513)-Net in Base 128
(19, 47, 513)-net in base 128, using
- t-expansion [i] based on (17, 47, 513)-net in base 128, using
- 25 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
- base change [i] based on digital (8, 63, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 63, 513)-net over F256, using
- 25 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
(47−28, 47, 564746)-Net in Base 128 — Upper bound on s
There is no (19, 47, 564747)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1093 628862 205742 286015 965660 096278 157306 182612 747003 826947 377749 355405 290087 022304 228797 200261 407872 > 12847 [i]