Best Known (53−45, 53, s)-Nets in Base 2
(53−45, 53, 11)-Net over F2 — Constructive and digital
Digital (8, 53, 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
(53−45, 53, 14)-Net in Base 2 — Upper bound on s
There is no (8, 53, 15)-net in base 2, because
- 13 times m-reduction [i] would yield (8, 40, 15)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(240, 15, S2, 3, 32), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 13 194139 533312 / 11 > 240 [i]
- extracting embedded OOA [i] would yield OOA(240, 15, S2, 3, 32), but