Best Known (32, 32+41, s)-Nets in Base 8
(32, 32+41, 69)-Net over F8 — Constructive and digital
Digital (32, 73, 69)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 23, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- digital (9, 50, 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 (3, 23, 24)-net over F8, using
(32, 32+41, 97)-Net over F8 — Digital
Digital (32, 73, 97)-net over F8, using
- t-expansion [i] based on digital (28, 73, 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
(32, 32+41, 2102)-Net in Base 8 — Upper bound on s
There is no (32, 73, 2103)-net in base 8, because
- 1 times m-reduction [i] would yield (32, 72, 2103)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 105540 207116 050595 506293 197115 805902 446978 221957 872639 672062 125921 > 872 [i]