Best Known (8, 8+56, s)-Nets in Base 8
(8, 8+56, 35)-Net over F8 — Constructive and digital
Digital (8, 64, 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]
(8, 8+56, 75)-Net in Base 8 — Upper bound on s
There is no (8, 64, 76)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(864, 76, S8, 56), but
- the linear programming bound shows that M ≥ 598 374671 077432 840156 694938 169093 962167 338597 071717 850766 556341 993472 / 86578 775041 > 864 [i]