Information on Result #1878842
There is no digital (11, 11+k, 45)-net over F4 for arbitrarily large k, because logical equivalence would yield (11, m, 45)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (11, 131, 45)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4131, 45, S4, 3, 120), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1452 495967 392894 355393 274435 948981 116111 418687 645795 235310 955933 795262 298203 357184 / 121 > 4131 [i]
- extracting embedded OOA [i] would yield OOA(4131, 45, S4, 3, 120), 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.