Best Known (70, 70+157, s)-Nets in Base 2
(70, 70+157, 49)-Net over F2 — Constructive and digital
Digital (70, 227, 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]
(70, 70+157, 102)-Net in Base 2 — Upper bound on s
There is no (70, 227, 103)-net in base 2, because
- 28 times m-reduction [i] would yield (70, 199, 103)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2199, 103, S2, 2, 129), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 12 855504 354071 922204 335696 738729 300820 177623 950262 342682 411008 / 13 > 2199 [i]
- extracting embedded OOA [i] would yield OOA(2199, 103, S2, 2, 129), but