On Proinov’s Lower Bound for the Diaphony

[1] BILYK, D.: On Roth’s orthogonal function method in discrepancy theory, Unif. Distrib. Theory 6 (2011), no. 1, 143–184.Search in Google Scholar

[2] CRISTEA, L. L.—PILLICHSHAMMER, F.: A lower bound for the b−adic diaphony, Rend. Mat. Appl. Ser. VII 27 (2007), 147-153.Search in Google Scholar

[3] DICK, J.—PILLICHSHAMMER, F.: Digital Nets and Sequences. Discrepancy Theory and Quasi-Monte Carlo Integration, Cambridge University Press, Cambridge, 2010.10.1017/CBO9780511761188Search in Google Scholar

[4] DICK, J.—PILLICHSHAMMER, F.: Explicit constructions of point sets and sequences with low discrepancy, (P. Kritzer, ed. et al.), In: Uniform Distribution and Quasi-Monte Carlo Methods. Discrepancy, Integration and Applications. Radon Ser. Comput. Appl. Math. Vol. 15, De Gruyter, Berlin 2014, pp. 63–86.10.1515/9783110317930.63Search in Google Scholar

[5] ERDŐS, P.—TURÁN, P.: On a problem in the theory of uniform distribution, Indag. Math. 10 (1948), 370–378.Search in Google Scholar

[6] FINE, N. J.: On the Walsh Functions, Trans. Amer. Math. Soc. 65, No. 3 (1949), 372–414.Search in Google Scholar

[7] GROZDANOV, V.—STOILOVA, S.: On the theory of b-adic diaphony, C. R. Acad. Bulgare Sci. 54 (2001), 31–34.Search in Google Scholar

[8] HELLEKALEK, P.—LEEB, H.: Dyadic diaphony, Acta. Arith. 80 (1997), no. 2, 187–196.Search in Google Scholar

[9] HINRICHS, A.—LARCHER, G.: An improved lower bound for the ℒ₂-discrepancy, J. Complexity 34 (2016), 68–77.10.1016/j.jco.2015.11.008Search in Google Scholar

[10] HINRICHS, A.—MARKHASIN, L.: On lower bounds for the ℒ₂-discrepancy, J. Complexity 27 (2011), 127–132.10.1016/j.jco.2010.11.002Search in Google Scholar

[11] KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences. In: Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974.Search in Google Scholar

[12] LARCHER, G.: On the star-discrepancy of sequences in the unit-interval, J. Complexity 31 (2015), no. 3, 474–485.Search in Google Scholar

[13] LARCHER, G.: On the discrepancy of sequences in the unit-interval, Indag. Math. (N.S.) 27 (2016), 546–558.10.1016/j.indag.2015.11.003Search in Google Scholar

[14] LARCHER, G.: Digital Point Sets: Analysis and Application. In: Random and Quasi-Random Point Sets, Lect. Notes in Stat. Vol. 138, Springer-Verlag, Berlin, 1998, pp. 167–222.Search in Google Scholar

[15] LARCHER, G.—PUCHHAMMER, F.: An improved bound for the star discrepancy of sequences in the unit interval, Unif. Distrib. Theory 11 (2016), no. 1, 1–14.Search in Google Scholar

[16] PAUSINGER, F.: On the intriguing search for good permutations, Unif. Distrib. Theory 14 (2019), no. 1, 53–86.Search in Google Scholar

[17] PROINOV, P. D.: On irregularities of distribution, C.R. Acad. Bulgare Sci. 39 (1986), no. 9, 31–34.Search in Google Scholar

[18] PROINOV, P. D.: Quantitative Theory of Uniform Distribution and Integral Approximation, University of Plovdiv, Bulgaria (2000). (In Bulgarian)Search in Google Scholar

[19] PROINOV, P. D.: On extreme and ℒ₂-discrepancies of symmetric finite sequences, Serdica Math. J. 10 (1984), 376–383.Search in Google Scholar

[20] PROINOV, P. D.: On the ℒ₂-discrepancy of some infinite sequences, Serdica Math. J. 11, (1985), 3–12.Search in Google Scholar

[21] ROTH, K. F.: On irregularities of distribution, Mathematika 1 (1954), 73–79.10.1112/S0025579300000541Search in Google Scholar

[22] VAN DER CORPUT, J. G.: Verteilungsfunktionen I, Proc. Akad. Amsterdam 38 (1935), 813–821. (In German)Search in Google Scholar

[23] VAN DER CORPUT, J. G.: Verteilungsfunktionen II, Proc. Akad. Amsterdam 38 (1935), 1058–1066. (In German)Search in Google Scholar

[24] WALSH, J. L.: A closed set of normal orthogonal functions, Amer. J. Math. 55 (1923), 5–24.10.2307/2387224Search in Google Scholar

[25] WEYL, H.: Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), no. 3, 313–352. (In German)Search in Google Scholar

[26] ZINTERHOF, P.:Über einige Abschätzungen bei der Approximation von Funktionen mit Gleichverteilungsmethoden, Sitzungsber. Österr. Akad. Wiss. Math.-Naturwiss. Kl. S.-B. II 185 (1976), 121–132. (In German)Search in Google Scholar