Information on Result #1878342
There is no digital (12, 12+k, 34)-net over F3 for arbitrarily large k, because logical equivalence would yield (12, m, 34)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (12, 97, 34)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(397, 34, S3, 3, 85), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 858962 534553 352218 394101 882942 702121 170179 203335 / 43 > 397 [i]
- extracting embedded OOA [i] would yield OOA(397, 34, S3, 3, 85), 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.