Best Known (57−51, 57, s)-Nets in Base 2
(57−51, 57, 10)-Net over F2 — Constructive and digital
Digital (6, 57, 10)-net over F2, using
- net from sequence [i] based on digital (6, 9)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 6 and N(F) ≥ 10, using
(57−51, 57, 11)-Net in Base 2 — Upper bound on s
There is no (6, 57, 12)-net in base 2, because
- 14 times m-reduction [i] would yield (6, 43, 12)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(243, 12, S2, 4, 37), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 175 921860 444160 / 19 > 243 [i]
- extracting embedded OOA [i] would yield OOA(243, 12, S2, 4, 37), but