Computing bounds for the star discrepancy (Q1592539)

The author presents on algorithm to compute upper bounds for the star discrepancy of an arbitrary set of \(n\) points in the \(s\)-dimensional unit cube. For an integer \(k\geq 1\), this algorithm computes in \({\mathcal O}(ns\log k+2^s k^2)\) time and \({\mathcal O}(k^s)\) space a bound that is no better than a function depending on \(k\) and \(s\). As an application, new upper bounds for the star discrepancy of some Faure \((0,m,s)\)-nets for \(s\in\{7, \dots, 20\}\) are given.