The notion of symmetrization, also known as Davenport’s reflec- tion principle, is well known in the area of the discrepancy theory and quasi- Monte Carlo (QMC) integration. In this paper we consider applying a sym- metrization technique to a certain class of QMC point sets called digital nets over Z b. Although symmetrization has been recognized as a geometric technique in the multi-dimensional unit cube, we give another look at symmetrization as a geometric technique in a compact totally disconnected abelian group with dyadic arithmetic operations. Based on this observation we generalize the notion of sym- metrization from base 2 to an arbitrary base b ∈ N, b ≥ 2. Subsequently, we study the QMC integration error of symmetrized digital nets over Z b in a reproducing kernel Hilbert space. The result can be applied to component-by-component con- struction or Korobov construction for finding good symmetrized (higher order) polynomial lattice rules which achieve high order convergence of the integration error for smooth integrands at the expense of an exponential growth of the num- ber of points with the dimension. Moreover, we consider two-dimensional sym- metrized Hammersley point sets in prime base b, and prove that the minimum Dick weight is large enough to achieve the best possible order of L p discrepancy for all 1 ≤ p < ∞.