  We consider the problem of finding a set (partial covering array) $S$ of
vertices of the Boolean $n$-cube having cardinality $2^{n-k}$ and intersecting
with maximum number of $k$-dimensional faces. We prove that the ratio between
the numbers of the $k$-faces containing elements of $S$ to $k$-faces is less
than $1-\frac{1+o(1)}{\sqrt{2\pi k}}$ as $n\rightarrow\infty$ for sufficiently
large $k$. The solution of the problem in the class of linear codes is found.
Connections between this problem, cryptography and an efficiency of
quantization are discussed.
