The Faure sequences are a popular class of low-discrepancy sequences. Their generalized variants, with better equi-distributionproperties,
are extensively used in quasi-Monte Carlo methods, especially for very high dimensional problems. The task of generating these
sequences can take substantial part of the overall CPU time of a quasi-Monte Carlo computation.
We present an efficient algorithm for generating these sequences, and demonstrate how it may be tuned to use the extended
instruction sets, available on many modern CPUs, to reduce drastically the CPU-time, spent for generating these sequences.
Supported by the project of European Commission – BIS 21 under contract ICA1-CT-2000-70016 and by the Ministry of Education
and Science of Bulgaria under contract NSF I-1201/02 and NSF MM-902/99.