Best Known (10, 10+67, s)-Nets in Base 8
(10, 10+67, 46)-Net over F8 — Constructive and digital
Digital (10, 77, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
(10, 10+67, 89)-Net in Base 8 — Upper bound on s
There is no (10, 77, 90)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(877, 90, S8, 67), but
- the linear programming bound shows that M ≥ 5 577865 509622 768193 121286 877945 364037 726733 563080 454026 031585 913232 748928 040960 / 1376 178407 > 877 [i]