Faure, H. On the star-discrepancy of generalized Hammersley sequences in two dimensions. (English) Zbl 0588.10060 Monatsh. Math. 101, 291-300 (1986). From a previous study in one dimension, precise estimates are deduced for the star discrepancy of some generalized Hammersley sequences in two dimensions, giving the lower constants presently known; also general bounds are obtained, and it is shown that these bounds are reached by the usual Hammersley sequences. Cited in 9 Documents MSC: 11K06 General theory of distribution modulo \(1\) Keywords:precise estimates; star discrepancy; generalized Hammersley sequences in two dimensions; lower constants × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Béjian, R., Faure, H.: Discrépance de la suite de Van Der Corput. C. R. Acad. Sci. Paris285-A, 313–316 (1977). [2] Braaten, E., Weller, G.: An improved low-discrepancy sequence for multidimensional quasi-Monte-Carlo integration. J. Comp. Physics33, 249–258 (1979). · Zbl 0426.65001 · doi:10.1016/0021-9991(79)90019-6 [3] De Clerck, L.: A method for exact calculation of the star-discrepancy of plane sets applied to the sequences of Hammersley. Mh. Math. To apear (1986). · Zbl 0588.10059 [4] Faure, H.: Discrépances de suites associées à un système de numération (en dimension un). Bull. Soc. Math. France109, 143–182 (1981). · Zbl 0488.10052 [5] Faure, H.: Discrépance de suites associées à un système de numération (en dimensions). Acta Arith.42, 337–351 (1982). · Zbl 0442.10035 [6] Faure, H.: Suites à faible discrépance dansT S . Publ. de l’Université de Limoges. 1980. [7] Haber, S. On a sequence of points of interest for numerical quadrature. J. Res. Nat. Bur. Standars Sect. B70, 127–136 (1966). · Zbl 0158.16002 [8] Halton, J. H., Zaremba, S. K.: The extreme andL 2-discrepancies of some plane sets. Mh. Math.73, 316–328 (1969). · Zbl 0183.31401 · doi:10.1007/BF01298982 [9] Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. New York: J. Wiley. 1974. · Zbl 0281.10001 [10] Roth, K. F.: Irregularities of distribution. Mathematika I, part 2, 73–79 (1954). · Zbl 0057.28604 · doi:10.1112/S0025579300000541 [11] Schmidt, W. M.: Irregularities of distribution VII. Acta Arith.21, 45–50 (1972). · Zbl 0244.10035 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.