Best Known (178−139, 178, s)-Nets in Base 2
(178−139, 178, 33)-Net over F2 — Constructive and digital
Digital (39, 178, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
(178−139, 178, 52)-Net in Base 2 — Upper bound on s
There is no (39, 178, 53)-net in base 2, because
- 26 times m-reduction [i] would yield (39, 152, 53)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2152, 53, S2, 3, 113), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 502391 187832 497878 132516 661246 222288 006726 811648 / 57 > 2152 [i]
- extracting embedded OOA [i] would yield OOA(2152, 53, S2, 3, 113), but