Best Known (55, 55+138, s)-Nets in Base 2
(55, 55+138, 42)-Net over F2 — Constructive and digital
Digital (55, 193, 42)-net over F2, using
- t-expansion [i] based on digital (54, 193, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
(55, 55+138, 82)-Net in Base 2 — Upper bound on s
There is no (55, 193, 83)-net in base 2, because
- 34 times m-reduction [i] would yield (55, 159, 83)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2159, 83, S2, 2, 104), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 23 384026 197294 446691 258957 323460 528314 494920 687616 / 21 > 2159 [i]
- extracting embedded OOA [i] would yield OOA(2159, 83, S2, 2, 104), but