This is page 1 Printer: Opaque this A new permutation choice in Halton sequences Bruno TUFFIN 1 ABSTRACT This paper has several folds. We make first new permu- tation choices in Halton sequences to improve their distributions. These choices are multi-dimensional and they are made for two different discrep- ancies. We show that multi-dimensional choices are better for standard quasi-Monte Carlo methods. We also use these sequences as a variance re- duction technique in Monte Carlo methods, which greatly improves the convergence accuracy of the estimators. For this kind of use, we observe that one-dimensional choices are more efficient. 1 Introduction Quasi-Monte Carlo methods are deterministic analogs of Monte Carlo ones. For the latters, convergence is in O(1/ √ N ) for an approximation with N random points. It is possible to construct a sequence where the points are deterministic and “well distributed” all over the integration space, for which the convergence speed is faster (in O(N -1 (log N ) s ) for dimension s). Hal- ton sequences verify this property. In this paper we give new permutation choices for Halton sequences to improve their distribution. Next, as the major problem encountered with quasi-Monte Carlo methods is the error bound evaluation, we use the sequences in Monte Carlo methods to obtain a variance reduction. In this case, we observe that a one-dimensional choice of permutations is more efficient. This paper is organized as follows: Section 2 describes quasi-Monte Carlo methods and Halton sequences and section 3 proposes a new choice of permutations in Halton sequences. Section 4 describes the use of such se- quences as a variance reduction in Monte Carlo methods and explain why a one-dimensional choice is better for this kind of use. Finally we conclude in Section 5. 1 IRISA, Campus de Beaulieu, 35042 Rennes cdex, France