Best Known (10, 10+40, s)-Nets in Base 8
(10, 10+40, 46)-Net over F8 — Constructive and digital
Digital (10, 50, 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+40, 196)-Net in Base 8 — Upper bound on s
There is no (10, 50, 197)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(850, 197, S8, 40), but
- the linear programming bound shows that M ≥ 18460 687874 096550 285508 470280 421966 444467 129920 221504 592935 046475 279897 845573 129713 873739 486442 867916 800000 / 12 247385 703695 406196 050675 706447 655918 400632 895231 448327 496743 > 850 [i]