Best Known (31−29, 31, s)-Nets in Base 2
(31−29, 31, 6)-Net over F2 — Constructive and digital
Digital (2, 31, 6)-net over F2, using
- net from sequence [i] based on digital (2, 5)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 2 and N(F) ≥ 6, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
(31−29, 31, 6)-Net in Base 2 — Upper bound on s
There is no (2, 31, 7)-net in base 2, because
- 21 times m-reduction [i] would yield (2, 10, 7)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(210, 7, S2, 3, 8), but
- the linear programming bound for OOAs shows that M ≥ 1 314304 / 1193 > 210 [i]
- extracting embedded OOA [i] would yield OOA(210, 7, S2, 3, 8), but