A survey on M. B. Levin's proofs for the exact lower discrepancy bounds of special sequences and point sets

Abstract

The goal of this overview article is to give a tangible presentation of recent breakthrough works in discrepancy theory by M. B. Levin. These works provide proofs for the exact lower discrepancy bounds of Halton's sequence and a certain class of $(t, s)$-sequences. Our survey aims at highlighting the major ideas of the proofs and we discuss further implications of the employed methods. Moreover, we derive extensions of Levin's results.