Best Known (7, 7+18, s)-Nets in Base 2
(7, 7+18, 10)-Net over F2 — Constructive and digital
Digital (7, 25, 10)-net over F2, using
- t-expansion [i] based on digital (6, 25, 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+18, 14)-Net in Base 2 — Upper bound on s
There is no (7, 25, 15)-net in base 2, because
- 3 times m-reduction [i] would yield (7, 22, 15)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(222, 15, S2, 3, 15), but
- the linear programming bound for OOAs shows that M ≥ 136613 832584 881917 394944 / 32070 152145 568877 > 222 [i]
- extracting embedded OOA [i] would yield OOA(222, 15, S2, 3, 15), but