Information on Result #1877906
There is no digital (55, 55+k, 65)-net over F2 for arbitrarily large k, because logical equivalence would yield (55, m, 65)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (55, 381, 65)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2381, 65, S2, 6, 326), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 827 442130 124284 063457 859842 103015 889906 674524 679774 380026 914161 489160 157201 441422 839699 591352 583228 456939 187796 443136 / 109 > 2381 [i]
- extracting embedded OOA [i] would yield OOA(2381, 65, S2, 6, 326), 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.