On the Scrambled Sobol Sequence

The Soból sequence is the most popular quasirandom sequence because of its simplicity and efficiency in implementation. We summarize aspects of the scrambling technique applied to Soból 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 Soból 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.