Best Known (5, 5+∞, s)-Nets in Base 2
(5, 5+∞, 9)-Net over F2 — Constructive and digital
Digital (5, m, 9)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 5 and N(F) ≥ 9, using
(5, 5+∞, 10)-Net in Base 2 — Upper bound on s
There is no (5, m, 11)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (5, 23, 11)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(223, 11, S2, 3, 18), but
- the linear programming bound for OOAs shows that M ≥ 1644 167168 / 183 > 223 [i]
- extracting embedded OOA [i] would yield OOA(223, 11, S2, 3, 18), but