Best Known (39−31, 39, s)-Nets in Base 8
(39−31, 39, 35)-Net over F8 — Constructive and digital
Digital (8, 39, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
(39−31, 39, 169)-Net in Base 8 — Upper bound on s
There is no (8, 39, 170)-net in base 8, because
- 1 times m-reduction [i] would yield (8, 38, 170)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 22526 125023 290078 601234 702101 020400 > 838 [i]