Best Known (31−22, 31, s)-Nets in Base 2
(31−22, 31, 12)-Net over F2 — Constructive and digital
Digital (9, 31, 12)-net over F2, using
- net from sequence [i] based on digital (9, 11)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 9 and N(F) ≥ 12, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
(31−22, 31, 18)-Net in Base 2 — Upper bound on s
There is no (9, 31, 19)-net in base 2, because
- 3 times m-reduction [i] would yield (9, 28, 19)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(228, 19, S2, 2, 19), but
- the linear programming bound for OOAs shows that M ≥ 21501 452180 765571 809280 / 74 685598 169693 > 228 [i]
- extracting embedded OOA [i] would yield OOA(228, 19, S2, 2, 19), but