Best Known (16, 16+26, s)-Nets in Base 128
(16, 16+26, 321)-Net over F128 — Constructive and digital
Digital (16, 42, 321)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 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, 29, 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, 13, 129)-net over F128, using
(16, 16+26, 386)-Net over F128 — Digital
Digital (16, 42, 386)-net over F128, using
- t-expansion [i] based on digital (15, 42, 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
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
(16, 16+26, 513)-Net in Base 128
(16, 42, 513)-net in base 128, using
- 22 times m-reduction [i] based on (16, 64, 513)-net in base 128, using
- base change [i] based on digital (8, 56, 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, 56, 513)-net over F256, using
(16, 16+26, 286749)-Net in Base 128 — Upper bound on s
There is no (16, 42, 286750)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 31829 714944 924041 819146 940759 949359 621079 978111 221426 335314 106136 281716 859320 633700 446101 > 12842 [i]