Information on Result #1877912
There is no digital (58, 58+k, 68)-net over F2 for arbitrarily large k, because logical equivalence would yield (58, m, 68)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (58, 399, 68)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2399, 68, S2, 6, 341), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 103 289995 123476 343586 236766 880120 474973 188231 713168 940513 226374 261625 904880 673647 785185 814131 205513 257436 126878 909899 735040 / 57 > 2399 [i]
- extracting embedded OOA [i] would yield OOA(2399, 68, S2, 6, 341), 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.