Best Known (128−71, 128, s)-Nets in Base 8
(128−71, 128, 100)-Net over F8 — Constructive and digital
Digital (57, 128, 100)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 43, 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 (14, 85, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (8, 43, 35)-net over F8, using
(128−71, 128, 144)-Net over F8 — Digital
Digital (57, 128, 144)-net over F8, using
- t-expansion [i] based on digital (45, 128, 144)-net over F8, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 45 and N(F) ≥ 144, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
(128−71, 128, 3737)-Net in Base 8 — Upper bound on s
There is no (57, 128, 3738)-net in base 8, because
- 1 times m-reduction [i] would yield (57, 127, 3738)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 4 961516 435994 549256 745535 734864 571190 921815 815869 777207 922831 978764 534670 795286 293361 819624 894937 657168 392819 287312 > 8127 [i]