Best Known (53−43, 53, s)-Nets in Base 8
(53−43, 53, 46)-Net over F8 — Constructive and digital
Digital (10, 53, 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]
(53−43, 53, 188)-Net in Base 8 — Upper bound on s
There is no (10, 53, 189)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(853, 189, S8, 43), but
- the linear programming bound shows that M ≥ 1 791787 809951 972270 084098 034216 665466 905352 144039 311980 252147 138509 319454 590241 785292 219575 346778 937185 040953 507840 / 2 298764 781336 997635 259666 949955 836308 197591 416300 931264 031329 092687 > 853 [i]