A central problem in discrepancy theory is the challenge of evenly distributing points [x1,...,Xn] in [0,1]~d. Suppose a set is so regular that for some ε > 0 and all y ∈ [0,1 ]~d the sub-region [0, y] = [0, y] x ? ?? x [0, y_d] contains a number of points nearly proportional to its volume and Vy∈[0,l]d 1/n#{1 < i < n : x_i ∈ [0, y]} - vol([0, y]) < ∈, how large does n have to be depending on d and ε? We give an elementary proof of the currently best known result, due to Hinrichs, showing that n?d·ε~(-1).
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