Best Known (17, 17+25, s)-Nets in Base 128
(17, 17+25, 345)-Net over F128 — Constructive and digital
Digital (17, 42, 345)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 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, 30, 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, 12, 129)-net over F128, using
(17, 17+25, 405)-Net over F128 — Digital
Digital (17, 42, 405)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12842, 405, F128, 25) (dual of [405, 363, 26]-code), using
- 17 step Varšamov–Edel lengthening with (ri) = (2, 16 times 0) [i] based on linear OA(12840, 386, F128, 25) (dual of [386, 346, 26]-code), using
- extended algebraic-geometric code AGe(F,360P) [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- 17 step Varšamov–Edel lengthening with (ri) = (2, 16 times 0) [i] based on linear OA(12840, 386, F128, 25) (dual of [386, 346, 26]-code), using
(17, 17+25, 407)-Net in Base 128 — Constructive
(17, 42, 407)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 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, 29, 257)-net in base 128, using
- 3 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
- 3 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- digital (1, 13, 150)-net over F128, using
(17, 17+25, 513)-Net in Base 128
(17, 42, 513)-net in base 128, using
- 30 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+25, 659459)-Net in Base 128 — Upper bound on s
There is no (17, 42, 659460)-net in base 128, because
- 1 times m-reduction [i] would yield (17, 41, 659460)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 248 664276 232080 312343 327088 258218 204342 005420 436263 479577 674650 684037 581471 871809 207296 > 12841 [i]