New star discrepancy bounds for $$(t,m,s)$$-nets and $$(t,s)$$-sequences

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.

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