Best Known (47, 47+52, s)-Nets in Base 8
(47, 47+52, 99)-Net over F8 — Constructive and digital
Digital (47, 99, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 33, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (14, 66, 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 (7, 33, 34)-net over F8, using
(47, 47+52, 144)-Net over F8 — Digital
Digital (47, 99, 144)-net over F8, using
- t-expansion [i] based on digital (45, 99, 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
(47, 47+52, 4122)-Net in Base 8 — Upper bound on s
There is no (47, 99, 4123)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 255118 680688 081706 420655 187515 818844 458380 283504 535832 287760 787124 739567 557805 175161 489297 > 899 [i]