Information on Result #1868326
There is no (31, 31+k, 40)-net in base 2 for arbitrarily large k, because logical equivalence would yield (31, m, 40)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (31, 192, 40)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2192, 40, S2, 5, 161), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 200867 255532 373784 442745 261542 645325 315275 374222 849104 412672 / 27 > 2192 [i]
- extracting embedded OOA [i] would yield OOA(2192, 40, S2, 5, 161), 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.