  We discuss construction of coverings of the unit ball of a finite dimensional
Banach space. The well known technique of comparing volumes gives upper and
lower bounds on covering numbers. This technique does not provide a
construction of good coverings. Here we apply incoherent dictionaries for
construction of good coverings. We use the following strategy. First, we build
a good covering by balls with a radius close to one. Second, we iterate this
construction to obtain a good covering for any radius. We mostly concentrate on
the first step of this strategy.
