A covering array CA(n,k,g) is a k x n array on a set of g symbols with
the property that in every pair of rows, every pair of symbols appears
in at least one column. The smallest n for which a CA(n,k,g) exists
for a fixed k and g is denoted by CAN(k,g). For g=2 a row in a
covering array can be considered as the characteristic vector for a
subset of an n-set. Using this, the value of CAN(k,2) can be found
with the well-known Erdos-Ko-Rado theorem.  For g>2 a row in a
covering array can be considered as the characteristic vector of a
g-partition of an n-set.  I have been working on generalizations of
the Erdos-Ko-Rado theorem to partitions try to solve for CAN(k,g),
for general g. In this talk, I will outline the proof of one such
higher-order generalization of the Erdos-Ko-Rado theorem for
systems of g-partitions of an n-set. Time permitting, I will give
another possible generalizations and discuss the possible applications
to covering arrays.