A note on corner avoidance of random-start Halton sequences

Recently, the analysis of quasi-Monte Carlo (QMC) sampling of integrands with singularities gained considerable interest. In this setting error bounds for QMC integration, in addition to discrepancy, include a measure how well the singularities are avoided by the utilized sequences. The article aims to generalize results for the corner avoidance of the classical Halton sequence to Halton sequences that start in an arbritrary point of the unit cube. In particular, it is shown that almost all (in Lebesgue sense) random-start Halton sequences exhibit the same corner avoidance property as the original Halton sequence.