Points sets with low $L_p$ discrepancy
Mathematica slovaca, Tome 57 (2007) no. 1, pp. 11-32
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Kritzer, Peter; Pillichshammer, Friedrich. Points sets with low $L_p$ discrepancy. Mathematica slovaca, Tome 57 (2007) no. 1, pp. 11-32. http://geodesic.mathdoc.fr/item/MASLO_2007_57_1_a1/

[1] BECK J.-CHEN W. W. L.: Irregularitгes of Distribution. Cambridge Universitу Press, 1987. | MR

[2] CHEN W. W. L.-SKRIGANOV M. M.: Davenporťs theorem in the theory of irregularities of point distribution. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 269 (2000), 339-353. | MR

[3] DE CLERCK L.: A method for exact calculation of the stardiscrepancy of plane sets applied to the sequences of Hammersley. Monatsh. Math. 101 (1986), 261-278. | MR | Zbl

[4] DRMOTA M.-TICHY R. F.: Sequences, Discrepancies and Applications. Lecture Notes in Math. 1651, Springer-Verlag, Berlin, 1997. | MR | Zbl

[5] ENTACHER K.: Haar function based estimates of the star-discrepancy of plane digital nets. Monatsh. Math. 130 (2000), 99-108. | MR | Zbl

[6] HALTON J. H.-ZAREMBA S. K.: The extreme and the $L^2$ discrepancies of some plane sets. Monatsh. Math. 73 (1969), 316-328. | MR

[7] KRITZER P.: On some remarkable properties of the two-dimensional Hammersley point set in base 2 J. Théor. Nombres Bordeaux 18 (2006), 203-221. | MR

[8] KRITZER P.-LARCHER G.-PILLICHSHAMMER F.: A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets. Ann. Mat. Pura Appl. (4) (2007) (To appear). | MR | Zbl

[9] KUIPERS L.-NIEDERREITER H.: Uniform Distribution of Sequences. John Wileу, New York, 1974. | MR | Zbl

[10] LARCHER G.-PILLICHSHAMMER F.: Sums of distances to the nearest integer and the discrepancy of digital nets. Acta Arith. 106 (2003), 379-408. | MR | Zbl

[11] MATOUŠEK J.: Geometric Discrepancy. Algorithms Combin. 18, Springer, Berlin, 1999. | MR | Zbl

[12] NIEDERREITER H.: Point sets and sequences with small discrepancy. Monatsh. Math. 104 (1987), 273-337. | MR | Zbl

[13] NIEDERREITER H.: Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia, 1992. | MR | Zbl

[14] PILLICHSHAMMER F.: On the $L_p$-discrepancy of the Hammersley Point Set. Monatsh. Math. 136 (2002), 67-79. | MR | Zbl

[15] ROTH K. F.: On irregularities of distribution. Mathematika 1 (1954), 73-79. | MR | Zbl

[16] SCHMIDT W. M.: Irregularities of distribution X. ln: Number Thеory and Algebra, Acadеmic Prеss, Nеw York, 1977, pp. 311-329. | MR | Zbl

[17] VILENKIN I. V.: Plane nets of Integration. Zh. Vychisl. Mat. Mat. Fiz. 7 (1967), 189-196 [English translation in: Comput. Math. Math. Phys. 7 (1967), 258-267.] | MR | Zbl