Thin bases in additive number theory

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