Best Known (3, 3+12, s)-Nets in Base 2
(3, 3+12, 7)-Net over F2 — Constructive and digital
Digital (3, 15, 7)-net over F2, using
- net from sequence [i] based on digital (3, 6)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 3 and N(F) ≥ 7, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
(3, 3+12, 8)-Net in Base 2 — Upper bound on s
There is no (3, 15, 9)-net in base 2, because
- 4 times m-reduction [i] would yield (3, 11, 9)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(211, 9, S2, 3, 8), but
- the linear programming bound for OOAs shows that M ≥ 345088 / 161 > 211 [i]
- extracting embedded OOA [i] would yield OOA(211, 9, S2, 3, 8), but