The exponent of discrepancy is at most 1.4778
نویسندگان
چکیده
We study discrepancy with arbitrary weights in the L 2 norm over the d-dimensional unit cube. The exponent p * of discrepancy is defined as the smallest p for which there exists a positive number K such that for all d and all ε ≤ 1 there exist Kε −p points with discrepancy at most ε. It is well known that p * ∈ (1, 2]. We improve the upper bound by showing that p * ≤ 1.4778842. This is done by using relations between discrepancy and integration in the average case setting with the Wiener sheet measure. Our proof is not constructive. The known constructive bound on the exponent p * is 2.454.
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ورودعنوان ژورنال:
- Math. Comput.
دوره 66 شماره
صفحات -
تاریخ انتشار 1997