Abstract
In this manuscript we introduce and study an extended version of the minimal dispersion of point sets, which has recently attracted considerable attention. Given a set Pn={x1,…,xn}⊂[0,1]d and k∈{0,1,…,n}, we define the k-dispersion to be the volume of the largest box amidst a point set containing at most k points. The minimal k-dispersion is then given by the infimum over all possible point sets of cardinality n. We provide both upper and lower bounds for the minimal k-dispersion that coincide with the known bounds for the classical minimal dispersion for a surprisingly large range of k’s.
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