Best Known (10, 10+37, s)-Nets in Base 8
(10, 10+37, 46)-Net over F8 — Constructive and digital
Digital (10, 47, 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+37, 207)-Net in Base 8 — Upper bound on s
There is no (10, 47, 208)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(847, 208, S8, 37), but
- the linear programming bound shows that M ≥ 45710 488007 876092 654400 472399 166620 806691 213539 391318 481168 792353 709735 009494 824887 141659 574272 / 16335 797907 142967 500494 901553 152919 434118 385852 248779 > 847 [i]