Information on Result #1868302
There is no (19, 19+k, 27)-net in base 2 for arbitrarily large k, because logical equivalence would yield (19, m, 27)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (19, 128, 27)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2128, 27, S2, 5, 109), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25180 895152 149446 296289 720949 950847 647744 / 55 > 2128 [i]
- extracting embedded OOA [i] would yield OOA(2128, 27, S2, 5, 109), 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.