Best Known (47−39, 47, s)-Nets in Base 8
(47−39, 47, 35)-Net over F8 — Constructive and digital
Digital (8, 47, 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]
(47−39, 47, 146)-Net in Base 8 — Upper bound on s
There is no (8, 47, 147)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(847, 147, S8, 39), but
- the linear programming bound shows that M ≥ 10658 720588 727382 484490 428637 940629 852749 695620 139410 623454 749999 108387 857843 667751 912138 080256 000000 / 3789 073207 474878 345964 159475 523664 746037 065508 701143 611973 > 847 [i]