Best Known (53, 116, s)-Nets in Base 8
(53, 116, 100)-Net over F8 — Constructive and digital
Digital (53, 116, 100)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 39, 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, 77, 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, 39, 35)-net over F8, using
(53, 116, 144)-Net over F8 — Digital
Digital (53, 116, 144)-net over F8, using
- t-expansion [i] based on digital (45, 116, 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
(53, 116, 3953)-Net in Base 8 — Upper bound on s
There is no (53, 116, 3954)-net in base 8, because
- 1 times m-reduction [i] would yield (53, 115, 3954)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 71 952608 610923 792085 197250 045251 442841 155339 117176 949851 365125 945830 709559 552910 366395 920806 224500 395888 > 8115 [i]