Best Known (19, 19+32, s)-Nets in Base 128
(19, 19+32, 321)-Net over F128 — Constructive and digital
Digital (19, 51, 321)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 16, 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 (3, 35, 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 (0, 16, 129)-net over F128, using
(19, 19+32, 387)-Net over F128 — Digital
Digital (19, 51, 387)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12851, 387, F128, 4, 32) (dual of [(387, 4), 1497, 33]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(12847, 386, F128, 4, 32) (dual of [(386, 4), 1497, 33]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(4;F,1511P) [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(12847, 386, F128, 4, 32) (dual of [(386, 4), 1497, 33]-NRT-code), using
(19, 19+32, 513)-Net in Base 128
(19, 51, 513)-net in base 128, using
- t-expansion [i] based on (17, 51, 513)-net in base 128, using
- 21 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
- 21 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
(19, 19+32, 278904)-Net in Base 128 — Upper bound on s
There is no (19, 51, 278905)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 293582 885266 794990 143120 443041 996535 273496 904853 268075 762939 593800 642417 335629 966653 491711 451492 156230 284477 > 12851 [i]