Algorithm 823: Implementing scrambled digital sequences

Random scrambling of deterministic (t, m, s)-nets and (t, s)-sequences eliminates their inherent bias while retaining their low-discrepancy properties. This article describes an implementation of two types of random scrambling, one proposed by Owen and another proposed by Faure and Tezuka. The four different constructions of digital sequences implemented are those proposed by Sobol', Faure, Niederreiter, and Niederreiter and Xing. Because the random scrambling involves manipulating all digits of each point, the code must be written carefully to minimize the execution time. Computed root mean square discrepancies of the scrambled sequences are compared to known theoretical results. Furthermore, the performances of these sequences on various test problems are discussed.