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The Unreasonable Effectiveness of Quasirandom Sequences

I present a new low discrepancy quasirandom sequence that offers many substantial improvements over other popular sequences such as the Sobol and Halton sequences.

Figure 1a. Comparison of the various low discrepancy quasirandom sequences. Note that the newly proposed $R$-sequence produces more evenly spaced points than any of the other methods. Furthermore, all other current methods require careful selection of basis parameters, and if not chosen carefully can lead to degeneracy (eg top right).

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