Information on Result #1878386
There is no digital (34, 34+k, 80)-net over F3 for arbitrarily large k, because logical equivalence would yield (34, m, 80)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (34, 314, 80)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3314, 80, S3, 4, 280), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 241 601901 558808 255480 810106 750959 761525 496530 550725 667504 364320 172551 252618 533199 343528 859969 183401 331740 222554 999779 831546 868843 129811 039523 483186 441561 / 281 > 3314 [i]
- extracting embedded OOA [i] would yield OOA(3314, 80, S3, 4, 280), 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.