Best Known (7, 7+14, s)-Nets in Base 2
(7, 7+14, 10)-Net over F2 — Constructive and digital
Digital (7, 21, 10)-net over F2, using
- t-expansion [i] based on digital (6, 21, 10)-net over F2, using
- net from sequence [i] based on digital (6, 9)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 6 and N(F) ≥ 10, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (6, 9)-sequence over F2, using
(7, 7+14, 16)-Net in Base 2 — Upper bound on s
There is no (7, 21, 17)-net in base 2, because
- 1 times m-reduction [i] would yield (7, 20, 17)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(220, 17, S2, 2, 13), but
- the linear programming bound for OOAs shows that M ≥ 1592 524800 / 1417 > 220 [i]
- extracting embedded OOA [i] would yield OOA(220, 17, S2, 2, 13), but