Best Known (31−23, 31, s)-Nets in Base 2
(31−23, 31, 11)-Net over F2 — Constructive and digital
Digital (8, 31, 11)-net over F2, using
- net from sequence [i] based on digital (8, 10)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 8 and N(F) ≥ 11, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
(31−23, 31, 16)-Net in Base 2 — Upper bound on s
There is no (8, 31, 17)-net in base 2, because
- 5 times m-reduction [i] would yield (8, 26, 17)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(226, 17, S2, 2, 18), but
- the linear programming bound for OOAs shows that M ≥ 6 416681 140224 / 94045 > 226 [i]
- extracting embedded OOA [i] would yield OOA(226, 17, S2, 2, 18), but