Best Known (14, 14+25, s)-Nets in Base 128
(14, 14+25, 300)-Net over F128 — Constructive and digital
Digital (14, 39, 300)-net over F128, 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
- digital (1, 26, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (1, 13, 150)-net over F128, using
(14, 14+25, 353)-Net over F128 — Digital
Digital (14, 39, 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+25, 513)-Net in Base 128
(14, 39, 513)-net in base 128, using
- 9 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+25, 196054)-Net in Base 128 — Upper bound on s
There is no (14, 39, 196055)-net in base 128, because
- 1 times m-reduction [i] would yield (14, 38, 196055)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 118 574545 425744 153401 111284 065582 793531 396471 314698 587158 901014 548717 705484 303134 > 12838 [i]