New star discrepancy bounds for (t,m,s)-nets and (t,s)-sequences
Résumé
In this paper, we derive new general upper bounds on the star discrepancy of (t,m,s)-nets and (t,s)-sequences. These kinds of point sets are among the most widely used in quasi-Monte Carlo methods for numerical integration. By our new results, we improve on previous discrepancy bounds and prove a conjecture stated by the second author in an earlier paper.