Information on Result #1868344
There is no (40, 40+k, 49)-net in base 2 for arbitrarily large k, because logical equivalence would yield (40, m, 49)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (40, 286, 49)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2286, 49, S2, 6, 246), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 39288 535676 373144 730275 197603 598846 367936 035912 990469 677796 654174 559600 263990 136667 111424 / 247 > 2286 [i]
- extracting embedded OOA [i] would yield OOA(2286, 49, S2, 6, 246), but
Mode: Bound.
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.