## Block Design

For any power of a prime number and
any natural number there exist at least
subsets of
for which
each pair has less than elements in common.

The figure illustrates the case with the
pixels of each column corresponding to a subset.

In general, the number of subsets is asymptotically
optimal, as is evident from the upper bound
,
.

Lemma 2,Dissertation, Bonn, 1979