Information on Result #1878858
There is no digital (19, 19+k, 70)-net over F4 for arbitrarily large k, because logical equivalence would yield (19, m, 70)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (19, 206, 70)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4206, 70, S4, 3, 187), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 655767 521039 926610 160299 985568 508871 509777 445500 566969 530371 604912 210544 906420 855058 587696 756197 562568 810482 328823 171437 821952 / 47 > 4206 [i]
- extracting embedded OOA [i] would yield OOA(4206, 70, S4, 3, 187), 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.