Best Known (68, 68+88, s)-Nets in Base 8
(68, 68+88, 111)-Net over F8 — Constructive and digital
Digital (68, 156, 111)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (10, 54, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- digital (14, 102, 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 (10, 54, 46)-net over F8, using
(68, 68+88, 156)-Net over F8 — Digital
Digital (68, 156, 156)-net over F8, using
(68, 68+88, 161)-Net in Base 8
(68, 156, 161)-net in base 8, using
- base change [i] based on digital (29, 117, 161)-net over F16, using
- net from sequence [i] based on digital (29, 160)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 29 and N(F) ≥ 161, using
- net from sequence [i] based on digital (29, 160)-sequence over F16, using
(68, 68+88, 3895)-Net in Base 8 — Upper bound on s
There is no (68, 156, 3896)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 762 879440 047654 176082 140566 083510 646050 136037 896024 085819 780330 531636 943366 059097 925588 918280 532862 865102 412707 939052 376002 318197 708073 183178 > 8156 [i]