Abstract
It is shown that the existence theorems on good lattice points and optimal coefficients of Hlawka, Korobov and Niederreiter are essentially best possible.
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References
Hlawka, E.: Zur angenäherten Berechnung mehrfacher Integrale. Mh. Math.66, 140–151 (1962).
Korobov, N. M.: Numbertheoretical Methods in Approximate Analysis. Moscow: Fizmatgiz. 1963 (In Russian.)
Zaremba, S. K.: La méthode des “bons treillis” pour le calcul des intégrales multiples. In: Applications of Number Theory to Numerical Analysis. (S. K. Zaremba, ed.) pp. 39–119 New York: Academic Press. 1972.
Niederreiter, H.: Existence of Good Lattice Points in the Sense of Hlawka. Mh. Math.86, 203–219 (1978).
Larcher, G.: On the Distribution of Sequences connected with Good Lattice Points. Mh. Math.101, 135–150 (1986).
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Larcher, G. A best lower bound for good lattice points. Monatshefte für Mathematik 104, 45–51 (1987). https://doi.org/10.1007/BF01540524
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DOI: https://doi.org/10.1007/BF01540524