Best Known (89−85, 89, s)-Nets in Base 2
(89−85, 89, 8)-Net over F2 — Constructive and digital
Digital (4, 89, 8)-net over F2, using
- net from sequence [i] based on digital (4, 7)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 4 and N(F) ≥ 8, using
(89−85, 89, 9)-Net in Base 2 — Upper bound on s
There is no (4, 89, 10)-net in base 2, because
- 73 times m-reduction [i] would yield (4, 16, 10)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(216, 10, S2, 3, 12), but
- the linear programming bound for OOAs shows that M ≥ 83807 961088 / 1 262099 > 216 [i]
- extracting embedded OOA [i] would yield OOA(216, 10, S2, 3, 12), but