Information on Result #1877900
There is no digital (52, 52+k, 61)-net over F2 for arbitrarily large k, because logical equivalence would yield (52, m, 61)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (52, 419, 61)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2419, 61, S2, 7, 367), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 32 999913 962009 210059 679612 176995 930308 233961 773576 918466 689667 860098 337098 516662 383593 445385 150587 019591 753304 289166 046548 459520 / 23 > 2419 [i]
- extracting embedded OOA [i] would yield OOA(2419, 61, S2, 7, 367), 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.