Information on Result #1868848
There is no (31, 31+k, 74)-net in base 3 for arbitrarily large k, because logical equivalence would yield (31, m, 74)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (31, 290, 74)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3290, 74, S3, 4, 259), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 229 508652 590225 900915 193766 377529 564949 108466 983495 168600 256377 208056 541526 061551 978631 651838 527412 783227 454480 502657 288667 678716 723464 947451 / 65 > 3290 [i]
- extracting embedded OOA [i] would yield OOA(3290, 74, S3, 4, 259), but
Mode: Bound.
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.