Best Known (8, 63, s)-Nets in Base 8
(8, 63, 35)-Net over F8 — Constructive and digital
Digital (8, 63, 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, 63, 79)-Net in Base 8 — Upper bound on s
There is no (8, 63, 80)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(863, 80, S8, 55), but
- the linear programming bound shows that M ≥ 3966 400830 086595 787407 641320 388429 745929 812405 462998 489371 107039 117312 / 4 288529 412765 > 863 [i]