de Mathématiques de Luminy
Faure Henri, Lemieux Christiane.
Generalized Halton sequences in 2007: a comparative study.
Halton sequences (, 1960) have always been quite popular with practitioners, in part because of their intuitive definition and ease of implementation. However, in their original form, these sequences have also been known for their inadequacy to integrate functions in moderate to large dimensions, in which case (t, s)-sequences like the Sobol’ sequence  are usually preferred. To overcome this problem, one possible approach is to include permutations in the definition of Halton sequences—thereby obtaining generalized Halton sequences—an idea that goes back to almost thirty years ago [3, 6], and that has been studied by many researchers in the last few years. In parallel to these efforts, an important improvement in the upper bounds for the discrepancy of Halton sequences has been made by Atanassov in . Together, these two lines of research have revived the interest in Halton sequences, and the aim of this paper is to provide an up-to-date study of different generalized Halton sequences, and compare them through an extensive set of numerical experiments. In addition, we propose a new generalized Halton sequence that appears to be competitive with the best ones proposed so far.