Best Known (10, 10+41, s)-Nets in Base 8
(10, 10+41, 46)-Net over F8 — Constructive and digital
Digital (10, 51, 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+41, 191)-Net in Base 8 — Upper bound on s
There is no (10, 51, 192)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(851, 192, S8, 41), but
- the linear programming bound shows that M ≥ 85480 962111 564903 813875 397996 274325 543682 573399 200465 347315 868303 384657 782871 302838 695483 795316 932608 / 7 061995 081120 102290 718487 620053 610775 747837 362029 929429 > 851 [i]