Information on Result #1877956
There is no digital (80, 80+k, 90)-net over F2 for arbitrarily large k, because logical equivalence would yield (80, m, 90)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (80, 621, 90)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2621, 90, S2, 7, 541), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2889 118738 270890 832116 830774 483674 468735 793808 758777 421860 297996 411436 759020 387444 152761 561121 687516 644495 481068 484007 314965 534148 209849 196281 211010 261106 701850 246871 733871 390204 456771 518464 / 271 > 2621 [i]
- extracting embedded OOA [i] would yield OOA(2621, 90, S2, 7, 541), 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.