On a new class of pseudorandom numbers for simulation methods
The explicit inversive congruential method for generating pseudorandom numbers, introduced previously by \textit{J. Eichenauer-Herrmann} [Math. Comput. 60, No. 201, 375-384 (1993; Zbl 0795.65002)], is discussed. The resulting pseudorandom numbers possess optimal nonlinearity property and show the best possible behavior under the lattice test. It is guaranteed that they pass the serial test and thus have desirable independence properties. The discrepancy bounds are in good accordance with the law of the iterated logarithm for discrepancies. The method can easily generate a large number of parallel streams of pseudorandom numbers. The numbers satisfy the requirements of \textit{W. F. Eddy} [J. Comput. Appl. Math. 31, No. 1, 63-71 (1990; Zbl 0703.65007)] on random number generators for parallel processors.
scientific article; zbMATH DE number 773893
scientific article