Best Known (4, 4+9, s)-Nets in Base 8
(4, 4+9, 25)-Net over F8 — Constructive and digital
Digital (4, 13, 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
(4, 4+9, 159)-Net in Base 8 — Upper bound on s
There is no (4, 13, 160)-net in base 8, because
- 1 times m-reduction [i] would yield (4, 12, 160)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 69008 243081 > 812 [i]