  It is proved that for any two subsets $A$ and $B$ of an arbitrary finite
field $\Fq$ such that $|A||B|>q$ the identity $16AB=\Fq$ holds. Moreover, it is
established that for every subsets $X, Y\subset \Fq$ with the property
$|X||Y|\geqslant 2q$ the equality $8XY=\Fq$ holds.
