Best Known (17, 17+26, s)-Nets in Base 128
(17, 17+26, 342)-Net over F128 — Constructive and digital
Digital (17, 43, 342)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 14, 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 (3, 29, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (1, 14, 150)-net over F128, using
(17, 17+26, 386)-Net in Base 128 — Constructive
(17, 43, 386)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 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
- (4, 30, 257)-net in base 128, using
- 2 times m-reduction [i] based on (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
- 2 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- digital (0, 13, 129)-net over F128, using
(17, 17+26, 387)-Net over F128 — Digital
Digital (17, 43, 387)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12843, 387, F128, 2, 26) (dual of [(387, 2), 731, 27]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(12841, 386, F128, 2, 26) (dual of [(386, 2), 731, 27]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,745P) [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(12841, 386, F128, 2, 26) (dual of [(386, 2), 731, 27]-NRT-code), using
(17, 17+26, 513)-Net in Base 128
(17, 43, 513)-net in base 128, using
- 29 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
(17, 17+26, 416483)-Net in Base 128 — Upper bound on s
There is no (17, 43, 416484)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 4 074074 461643 281474 327047 156721 538631 252563 091387 299390 849471 619849 478289 584774 507911 795080 > 12843 [i]