In the paper under review the authors use Walsh functions over finite groups for obtaining the inequality of Erdös-Turan-Koksma for an arbitrary $s$-dimensional set in the terms of sums of these functions. As a consequence of the main result the order $O((\log M)^s)$ of the discrepancy of an arbitrary $s$-dimensional set is obtained. For a special set the authors find the exact value of its generalized $b$-adic diaphony. [Editorial remark: For an extended version, cf. Math. Balk., New Ser. 19, No. 3-4, 349‒366 (2005; Zbl 1088.11061).]
Reviewer: Petar Popivanov (Sofia)