Best Known (56−46, 56, s)-Nets in Base 8
(56−46, 56, 46)-Net over F8 — Constructive and digital
Digital (10, 56, 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]
(56−46, 56, 179)-Net in Base 8 — Upper bound on s
There is no (10, 56, 180)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(856, 180, S8, 46), but
- the linear programming bound shows that M ≥ 685 535481 247798 789299 057186 036943 504310 025650 951406 605994 117695 555171 026007 018029 407496 787616 670915 947040 604160 / 1 730954 210009 034837 781808 803919 045685 607266 333095 847743 284013 > 856 [i]