Explicit Formulation of the Generalized Antithetic Transformation for Monte Carlo Integration

Abstract

The method of "antithetic variates" for Monte Carlo sampling was invented by Hammersley and Morton, and has been generalized by Halton and Handscomb, and by Laurent, who described the most economical general transformations without giving their explicit forms (except for a few of the simplest cases). The present paper gives a derivation of the full explicit forms of the Laurent transforms of any order.