We will prove the following theorem on Walsh series, and we will derive from this theorem an effective and constructive method for the numerical integration of Walsh series by number-theoretic methods. Further, concrete computer calculations are given. Theorem. For base b > 2, dimension s > 1, and o > 1, c > 0 {b, s € N; c, a e R), let i,E~°(c) be the class of all functions f: [0, l)s -» C whic...