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AISTLEITNER, C.: Covering numbers, dyadic chaining and discrepancy,J. Complexity 27 (2011), 531–540.Search in Google Scholar
APOSTOL, T. M.: An Elementary View of Euler’s Summation Formula,Amer. Math. Monthly 106 (1999), no. 5, 409–418.Search in Google Scholar
CHEN, W. W. L.—SKRIGANOV, M. M.: Explicit constructions in the classical mean squares problem in irregularity of point distribution,J.Reine Angew. Math. 545 (2002), 67–95.Search in Google Scholar
CHO, Y.—KIM, S.: Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities, Electronic J. Linear Algebra 36 (2020), 228–255.Search in Google Scholar
DAVENPORT, H.: Note on irregularities of distribution,Mathematika 3 (1956), 131–135.Search in Google Scholar
DICK, J.—PILLICHSHAMMER, F.: Digital Nets and Sequences. Cambridge University Press, Cambridge, 2010.Search in Google Scholar
DICK, J.—PILLICHSHAMMER, F.: Explicit constructions of point sets and sequences with low discrepancy,In:Uniform distribution and quasi-Monte Carlo methods, Radon Ser. Comput. Appl. Math. Vol. 15, De Gruyter, Berlin, 2014. pp. 63–86.Search in Google Scholar
DICK, J.—PILLICHSHAMMER, F.: Optimal ℒ2-discrepancy bounds for higher order digital sequences over the finite field 𝔽2,Acta Arith. 162, (2014) no. 1, 65–99.Search in Google Scholar
DOERR, B.: A lower bound for the discrepancy of a random point set,J. Complexity 30 (2014), 16–20.Search in Google Scholar
GNEWUCH, M.—PASING, H.—WEISS, C.: A generalized Faulhaber inequality, improved bracketing covers and applications to discrepancy, Math. Comput 90 (2021), no. 332, 2873–2898.Search in Google Scholar
HEINRICH, S.—NOVAK, E.—WASILKOWSKI, G.—WOZNIAKOWSKI, H.: The inverse of the star-discrepancy depends linearly on the dimension,Acta Arith. 96 (2001), no. 3, 279–302.Search in Google Scholar
KIDERLEN, M.—PAUSINGER, F.: Discrepancy of stratified samples from partitions of the unit cube, Monatsh. Math. 195 (2022), 267–306.Search in Google Scholar
KIRK, N.: Several Problems in Discrepancy Theory: Lower Bounds and Stratified Sampling, PhD Thesis, Queen’s University Belfast, 2023.Search in Google Scholar
KIRK, N.—PAUSINGER, F.: On the expected ℒ2-discrepancy of jittered sampling,Unif. Distrib. Theory 18 (2023), no. 1, 65–82.Search in Google Scholar
KIDERLEN, M.—PAUSINGER, F.: On a partition with a lower expected ℒ2−discrepancy than classical jittered sampling,J. Complexity 70 (2022), Article ID 101616, 13 pp.Search in Google Scholar
ROTH,K.F.: On irregularities of distribution,Mathematika 1 (1954), 73–79.Search in Google Scholar