Abstract
We study distributions \(\mathcal{D}_N \) of N points in the unit square U 2 with minimal order of L 2-discrepancy ℒ2[\(\mathcal{D}_N \)] < C(log N)1/2, where the constant C is independent of N. We present an approach that uses Walsh functions and can be generalized to higher dimensions. Bibliography: 19 titles.
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Chen, W.W.L., Skriganov, M.M. Davenport's Theorem in the Theory of Irregularities of Point Distribution. Journal of Mathematical Sciences 115, 2076–2084 (2003). https://doi.org/10.1023/A:1022668317029
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DOI: https://doi.org/10.1023/A:1022668317029