Introduction to finite fields and their applications
Introduction to finite fields and their applications
An exhaustive analysis of multiplicative congruential random number generators with modulus 231-1
SIAM Journal on Scientific and Statistical Computing
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Parallel linear congruential generators with prime moduli
Parallel Computing
On the L2-discrepancy for anchored boxes
Journal of Complexity
Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
A New Efficient Algorithm for Generating the Scrambled Sobol' Sequence
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Algorithm 823: Implementing scrambled digital sequences
ACM Transactions on Mathematical Software (TOMS)
Parallel linear congruential generators with Sophie-Germain moduli
Parallel Computing
On the optimal Halton sequence
Mathematics and Computers in Simulation
Computers & Mathematics with Applications
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The Soboĺ sequence is the most popular quasirandom sequence because of its simplicity and efficiency in implementation. We summarize aspects of the scrambling technique applied to Soboĺ sequences and propose a new simpler modified scrambling algorithm, called the multi-digit scrambling scheme. Most proposed scrambling methods randomize a single digit at each iteration. In contrast, our multi-digit scrambling scheme randomizes one point at each iteration, and therefore is more efficient. After the scrambled Soboĺ sequence is produced, we use this sequence to evaluate a particular derivative security, and found that when this sequence is numerically tested, it is shown empirically to be far superior to the original unscrambled sequence.