Best Known (249−175, 249, s)-Nets in Base 2
(249−175, 249, 49)-Net over F2 — Constructive and digital
Digital (74, 249, 49)-net over F2, using
- t-expansion [i] based on digital (70, 249, 49)-net over F2, using
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, and 1 place with degree 2 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
(249−175, 249, 108)-Net in Base 2 — Upper bound on s
There is no (74, 249, 109)-net in base 2, because
- 39 times m-reduction [i] would yield (74, 210, 109)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2210, 109, S2, 2, 136), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 315936 875005 671560 093754 083051 011296 956685 286201 647333 762932 932608 / 137 > 2210 [i]
- extracting embedded OOA [i] would yield OOA(2210, 109, S2, 2, 136), but