Improved upper bounds on the star discrepancy of (t,m,s)-nets and (t,s)-sequences

The concepts of (t,m,s)-nets and (t,s)-sequences are among the best known classes of point sets in the theory of quasi-Monte Carlo methods. In this paper, we give new general upper bounds for the star discrepancy of (t,m,s)-nets and (t,s)-sequences. By these findings, we improve existing upper bounds on the discrepancy of such point sets and extend results that have been obtained for low-dimensional nets and sequences during the past years.