Information on Result #1878840
There is no digital (10, 10+k, 41)-net over F4 for arbitrarily large k, because logical equivalence would yield (10, m, 41)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (10, 119, 41)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4119, 41, S4, 3, 109), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 25 619282 439286 572778 957813 760772 318479 498516 504696 474892 763289 918742 986752 / 55 > 4119 [i]
- extracting embedded OOA [i] would yield OOA(4119, 41, S4, 3, 109), 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.