DIGITAL NETS AND SEQUENCES CONSTRUCTED OVER FINITE RINGS AND THEIR APPLICATION TO QUASI-MONTE CARLO INTEGRATION

A detailed study of digital (t,m,s)-nets and digital (T,s)-sequences c onstructed over finite rings is carried out We present general existen ce theorems for digital nets and sequences and also explicit construct ions. Special attention is devoted to the case where the finite ring i s a residue class ring of the integers. This study is motivated by the problem of numerical integration of multivariate Walsh series by quas i-Monte Carlo methods, for which we also provide a general error bound .