Best Known (14, 14+23, s)-Nets in Base 128
(14, 14+23, 321)-Net over F128 — Constructive and digital
Digital (14, 37, 321)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 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, 26, 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, 11, 129)-net over F128, using
(14, 14+23, 353)-Net over F128 — Digital
Digital (14, 37, 353)-net over F128, using
- net from sequence [i] based on digital (14, 352)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 14 and N(F) ≥ 353, using
(14, 14+23, 513)-Net in Base 128
(14, 37, 513)-net in base 128, using
- 11 times m-reduction [i] based on (14, 48, 513)-net in base 128, using
- base change [i] based on digital (8, 42, 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, 42, 513)-net over F256, using
(14, 14+23, 304457)-Net in Base 128 — Upper bound on s
There is no (14, 37, 304458)-net in base 128, because
- 1 times m-reduction [i] would yield (14, 36, 304458)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 7237 129052 936071 240752 934500 495091 095177 678277 754999 070960 859253 394291 228512 > 12836 [i]