Improved discrepancy bounds for hybrid sequences involving Halton sequences (Q2919668)

In this paper the author considers various hybrid sequences in the \(s+t\)-dimensional unit cube, where the \(s\)-dimensional component stems from the Halton sequence. In particular, he mixes the Halton sequences with, Kronecker sequences, explicit nonlinear congruential sequences, digital explicit inversive sequences, or recursive inversive sequences. In all these cases the author provides asymptotic upper bounds for the discrepancy. Moreover he manages to improve several of his former results, e.g. [\textit{H. Niederreiter}, Acta Arith. 138, No. 4, 373--398 (2009; Zbl 1268.11102); Monatsh. Math. 161, No. 2, 193--222 (2010; Zbl 1273.11117)] or [\textit{H. Niederreiter} and \textit{A. Winterhof}, Unif. Distrib. Theory 6, No. 1, 33--56 (2011; Zbl 1338.11074)].