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Direction numbers for generating Sobol' sequences that satisfy the so-called Property A in up to 1111 dimensions have previously been given in Joe and Kuo ACM Trans. Math. Software, 29 (2003), pp. 49–57. However, these Sobol' sequences may have poor two-dimensional projections. Here we provide a new set of direction numbers alleviating this problem. These are obtained by treating Sobol' sequences in d dimensions as (t, d) -sequences and then optimizing the t-values of the two-dimensional projections. Our target dimension is 21201.
Joe et al. (Tue,) studied this question.