Sobol' sequence generator
The Sobol' sequence is an example of a low-discrepancy sequence. Such sequences are often called quasi-random sequences as they are commonly used in place of uniformly distributed random numbers. One application of Sobol' sequences is in numerical multiple integration, that is, in the approximation of integrals of functions which may depend on hundreds or even thousands of variables. These multiple integrals arise in areas such as quantum physics, probability, and mathematical finance. How well a Sobol' sequence performs in numerical multiple integration is determined by the choice of direction numbers. In some applications it is believed that it is the low-dimensional projections of the sequence that are important. As a result, this project attempts to produce direction numbers that result in Sobol' sequences with good two-dimensional projections. Files containing direction numbers and a C++ program to generate the Sobol' sequences from the direction numbers are provided. This allows the approximation of integrals in up to 21201 variables.