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

Henri Faure (1) , Peter Kritzer (2)

1 IML - Institut de mathématiques de Luminy
2 IFM - Institut für Finanzmathematik

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.

Mots clés: Discrepancy; (t; m; s)-net; s)-sequence; Uniform distribution modulo one

Domaines: Théorie des nombres [math.NT]

Henri Faure, Peter Kritzer. New star discrepancy bounds for (t,m,s)-nets and (t,s)-sequences. Monatshefte für Mathematik, 2013, 172 (1), pp.55-75. ⟨10.1007/s00605-012-0470-1⟩. ⟨hal-01273601⟩