Best Known (128, 128+43, s)-Nets in Base 8
(128, 128+43, 1061)-Net over F8 — Constructive and digital
Digital (128, 171, 1061)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 29, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- digital (99, 142, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 71, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 71, 513)-net over F64, using
- digital (8, 29, 35)-net over F8, using
(128, 128+43, 11230)-Net over F8 — Digital
Digital (128, 171, 11230)-net over F8, using
(128, 128+43, large)-Net in Base 8 — Upper bound on s
There is no (128, 171, large)-net in base 8, because
- 41 times m-reduction [i] would yield (128, 130, large)-net in base 8, but