Information on Result #1877878
There is no digital (41, 41+k, 50)-net over F2 for arbitrarily large k, because logical equivalence would yield (41, m, 50)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (41, 292, 50)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2292, 50, S2, 6, 251), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 206886 466346 471243 136639 015229 077469 481789 758731 696650 455233 014387 554350 757213 884221 751296 / 21 > 2292 [i]
- extracting embedded OOA [i] would yield OOA(2292, 50, S2, 6, 251), but
Mode: Bound (linear).
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.