Best Known (44−28, 44, s)-Nets in Base 128
(44−28, 44, 300)-Net over F128 — Constructive and digital
Digital (16, 44, 300)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 15, 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, 29, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (1, 15, 150)-net over F128, using
(44−28, 44, 386)-Net over F128 — Digital
Digital (16, 44, 386)-net over F128, using
- t-expansion [i] based on digital (15, 44, 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
(44−28, 44, 513)-Net in Base 128
(16, 44, 513)-net in base 128, using
- 20 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
(44−28, 44, 199663)-Net in Base 128 — Upper bound on s
There is no (16, 44, 199664)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 521 484942 776800 525994 685001 718449 142287 759657 369970 318008 478975 783862 304000 956546 006703 517651 > 12844 [i]