Information on Result #1878358
There is no digital (20, 20+k, 51)-net over F3 for arbitrarily large k, because logical equivalence would yield (20, m, 51)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (20, 148, 51)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3148, 51, S3, 3, 128), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 849942 425175 634864 623503 912258 483220 932365 501948 614869 075922 026508 741245 / 43 > 3148 [i]
- extracting embedded OOA [i] would yield OOA(3148, 51, S3, 3, 128), 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.