Best Known (3, 3+15, s)-Nets in Base 8
(3, 3+15, 24)-Net over F8 — Constructive and digital
Digital (3, 18, 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
(3, 3+15, 71)-Net in Base 8 — Upper bound on s
There is no (3, 18, 72)-net in base 8, because
- 1 times m-reduction [i] would yield (3, 17, 72)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 2377 600481 087791 > 817 [i]