Best Known (20, 20+30, s)-Nets in Base 8
(20, 20+30, 65)-Net over F8 — Constructive and digital
Digital (20, 50, 65)-net over F8, using
- t-expansion [i] based on digital (14, 50, 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
(20, 20+30, 76)-Net over F8 — Digital
Digital (20, 50, 76)-net over F8, using
- net from sequence [i] based on digital (20, 75)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 20 and N(F) ≥ 76, using
(20, 20+30, 930)-Net in Base 8 — Upper bound on s
There is no (20, 50, 931)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1437 753211 149850 956009 951753 593144 036187 554976 > 850 [i]