Improved discrepancy bounds for hybrid sequences involving Halton sequences
Improved upper bounds for the star discrepancy of digital nets in dimension 3
Improvements of the discrepancy of the van der Corput sequence.
Improvements on the star discrepancy of (t,s)-sequences
Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators
Irreducible Sobol' sequences in prime power bases
Sobol' sequences are a popular family of low-discrepancy sequences, in spite of requiring primitive polynomials instead of irreducible ones in later constructions by Niederreiter and Tezuka. We introduce a generalization of Sobol' sequences that removes this shortcoming and that we believe has the potential of becoming useful for practical applications. Indeed, these sequences preserve two important properties of the original construction proposed by Sobol': their generating matrices are non-singular...
Irregularities for distribution IX
Irregularities of continuous distributions
This paper deals with a continuous analogon to irregularities of point distributions. If a continuous fonction where is a compact body, is interpreted as a particle’s movement in time, then the discrepancy measures the difference between the particle’s stay in a proper subset and the volume of the subset. The essential part of this paper is to give lower bounds for the discrepancy in terms of the arc length of , . Furthermore it is shown that these estimates are the best possible despite of...
Irregularities of Distribution. IV.
Irregularities of distribution of digital -sequences in prime base.
Irregularities of distribution. VI
Irregularities of Point Distributions Relative to Homothetic Convex Bodies I.