Information on Result #1879656
There is no digital (6, 6+k, 51)-net over F7 for arbitrarily large k, because logical equivalence would yield (6, m, 51)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (6, 99, 51)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(799, 51, S7, 2, 93), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 875812 076998 063930 757182 152801 734486 857625 591237 003207 471162 651133 531677 095424 480008 / 47 > 799 [i]
- extracting embedded OOA [i] would yield OOA(799, 51, S7, 2, 93), 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.