Best Known (4, 4+11, s)-Nets in Base 2
(4, 4+11, 8)-Net over F2 — Constructive and digital
Digital (4, 15, 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
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
(4, 4+11, 10)-Net in Base 2 — Upper bound on s
There is no (4, 15, 11)-net in base 2, because
- 1 times m-reduction [i] would yield (4, 14, 11)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(214, 11, S2, 3, 10), but
- the linear programming bound for OOAs shows that M ≥ 15982 657536 / 845071 > 214 [i]
- extracting embedded OOA [i] would yield OOA(214, 11, S2, 3, 10), but