A remark on constructive covering of a ball of finite-dimensional Banach space

We discuss a 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 study incoherent systems and apply them to the construction of good coverings. We use the following strategy. First, we build a good covering by balls with radius close to $1$. Second, we iterate this construction to obtain a good covering for any radius. We provide a greedy-type algorithm for such constructions. Bibliography: 5 titles.