Best Known (65−35, 65, s)-Nets in Base 8
(65−35, 65, 70)-Net over F8 — Constructive and digital
Digital (30, 65, 70)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (4, 21, 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, 44, 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, 21, 25)-net over F8, using
(65−35, 65, 97)-Net over F8 — Digital
Digital (30, 65, 97)-net over F8, using
- t-expansion [i] based on digital (28, 65, 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
(65−35, 65, 2564)-Net in Base 8 — Upper bound on s
There is no (30, 65, 2565)-net in base 8, because
- 1 times m-reduction [i] would yield (30, 64, 2565)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 6309 599788 305831 150236 599633 915221 498995 898215 987491 920256 > 864 [i]