Best Known (15, 15+26, s)-Nets in Base 128
(15, 15+26, 300)-Net over F128 — Constructive and digital
Digital (15, 41, 300)-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 (1, 27, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (1, 14, 150)-net over F128, using
(15, 15+26, 386)-Net over F128 — Digital
Digital (15, 41, 386)-net over F128, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
(15, 15+26, 513)-Net in Base 128
(15, 41, 513)-net in base 128, using
- 15 times m-reduction [i] based on (15, 56, 513)-net in base 128, using
- base change [i] based on digital (8, 49, 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, 49, 513)-net over F256, using
(15, 15+26, 197426)-Net in Base 128 — Upper bound on s
There is no (15, 41, 197427)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 248 672444 184671 618369 678407 204238 843243 994776 809810 226897 965246 298831 997546 823872 679864 > 12841 [i]