Best Known (48, 48+38, s)-Nets in Base 2
(48, 48+38, 35)-Net over F2 — Constructive and digital
Digital (48, 86, 35)-net over F2, using
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(48, 48+38, 38)-Net over F2 — Digital
Digital (48, 86, 38)-net over F2, using
(48, 48+38, 142)-Net in Base 2 — Upper bound on s
There is no (48, 86, 143)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(286, 143, S2, 38), but
- the linear programming bound shows that M ≥ 2355 082802 209483 564297 468890 996579 884948 393922 920448 / 29 230362 541891 690794 351737 > 286 [i]