Best Known (58, 58+72, s)-Nets in Base 8
(58, 58+72, 100)-Net over F8 — Constructive and digital
Digital (58, 130, 100)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 44, 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, 86, 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, 44, 35)-net over F8, using
(58, 58+72, 144)-Net over F8 — Digital
Digital (58, 130, 144)-net over F8, using
- t-expansion [i] based on digital (45, 130, 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
(58, 58+72, 3699)-Net in Base 8 — Upper bound on s
There is no (58, 130, 3700)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 2532 020662 745542 374884 265104 780198 041471 331440 026402 340180 285716 990975 842033 688560 430485 138403 627317 890502 986502 686292 > 8130 [i]