Best Known (22−13, 22, s)-Nets in Base 2
(22−13, 22, 12)-Net over F2 — Constructive and digital
Digital (9, 22, 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]
(22−13, 22, 22)-Net in Base 2 — Upper bound on s
There is no (9, 22, 23)-net in base 2, because
- extracting embedded OOA [i] would yield OOA(222, 23, S2, 2, 13), but
- the linear programming bound for OOAs shows that M ≥ 61 466776 436736 / 12 737557 > 222 [i]