Best Known (70−38, 70, s)-Nets in Base 8
(70−38, 70, 70)-Net over F8 — Constructive and digital
Digital (32, 70, 70)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (4, 23, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- digital (9, 47, 45)-net over F8, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- digital (4, 23, 25)-net over F8, using
(70−38, 70, 97)-Net over F8 — Digital
Digital (32, 70, 97)-net over F8, using
- t-expansion [i] based on digital (28, 70, 97)-net over F8, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
(70−38, 70, 2394)-Net in Base 8 — Upper bound on s
There is no (32, 70, 2395)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1654 905877 892607 616970 885171 024852 327093 591633 387104 428205 726400 > 870 [i]