Thin bases in additive number theory

The set AA of nonnegative integers is called a basis of order hh if every nonnegative integer can be represented as the sum of exactly hh not necessarily distinct elements of AA. An additive basis AA of order hh is called thin if there exists c>0c>0 such that the number of elements of AA not exceeding xx is less than cx1/hcx1/h for all x≥1x≥1. This paper describes a construction of Shatrovskii˘ of thin bases of order hh.