Best Known (56, 56+68, s)-Nets in Base 8
(56, 56+68, 100)-Net over F8 — Constructive and digital
Digital (56, 124, 100)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 42, 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, 82, 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, 42, 35)-net over F8, using
(56, 56+68, 144)-Net over F8 — Digital
Digital (56, 124, 144)-net over F8, using
- t-expansion [i] based on digital (45, 124, 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
(56, 56+68, 3780)-Net in Base 8 — Upper bound on s
There is no (56, 124, 3781)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 9656 621517 312973 858975 649617 063982 099383 441673 897042 622724 882019 305738 768847 045318 385544 777067 038829 952814 954220 > 8124 [i]