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Lower bound for the discrepancy in two dimensions. (Minoration de discrépance en dimension deux.) (French) Zbl 0841.11039

Summary: We get, for the first time, the exact order of magnitude for the discrepancy of a two-dimensional sequence independently constructed by I. M. Sobol’ [USSR Comput. Math. Math. Phys. 7 (1967), No. 4, 86-112 (1969); translation from Zh. Vychisl. Mat. Mat. Fiz. 7, 784-802 (1967; Zbl 0185.41103)] and S. Srinivasan [J. Number Theory 10, 421-429 (1978; Zbl 0393.10051)]. Moreover this sequence has the smallest discrepancy presently known in two dimensions.

MSC:

11K38 Irregularities of distribution, discrepancy