Best Known (59, 59+74, s)-Nets in Base 8
(59, 59+74, 100)-Net over F8 — Constructive and digital
Digital (59, 133, 100)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 45, 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, 88, 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, 45, 35)-net over F8, using
(59, 59+74, 144)-Net over F8 — Digital
Digital (59, 133, 144)-net over F8, using
- t-expansion [i] based on digital (45, 133, 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
(59, 59+74, 3667)-Net in Base 8 — Upper bound on s
There is no (59, 133, 3668)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1 303974 682206 536098 608477 823503 203598 638632 001794 852052 057175 005080 339898 467132 888862 440021 040345 811365 423354 888255 628600 > 8133 [i]