Information on Result #1878846
There is no digital (13, 13+k, 51)-net over F4 for arbitrarily large k, because logical equivalence would yield (13, m, 51)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (13, 149, 51)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4149, 51, S4, 3, 136), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 95 740690 887720 846054 616947 355240 773569 419014 502299 003779 898601 119655 921088 876825 190619 676672 / 137 > 4149 [i]
- extracting embedded OOA [i] would yield OOA(4149, 51, S4, 3, 136), 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.