论文信息 - Lower bounds for the discrepancy of inversive congruential pseudorandom numbers

Lower bounds for the discrepancy of inversive congruential pseudorandom numbers

The inversive congruential method is a uniform pseudorandom number generator which was introduced recently. For a prime modulus p the discrepancy D(k) of k-tuples of successive pseudorandom numbers generated by this method determines the statistical independence properties of these pseudorandom numbers. It was shown earlier by the author that D(k) O(p-1/2(logp)k) for 2 2.

Harald Niederreiter | H. Niederreiter

[1] J. Lehn,et al. Marsaglia’s lattice test and non-linear congruential pseudo random number generators , 1988 .

[2] H. Niederreiter,et al. Remarks on nonlinear congruential pseudorandom numbers , 1988 .

[3] H. Niederreiter. Nonlinear Methods for Pseudorandom Number and Vector Generation , 1992 .

[4] H. Niederreiter. Pseudo-random numbers and optimal coefficients☆ , 1977 .

[5] Harald Niederreiter,et al. Lower bounds for the discrepancy of inversive congruential pseudorandom numbers with power of two modulus , 1992 .

[6] Jürgen Eichenauer-Herrmann,et al. Inversive congruential pseudorandom numbers : a tutorial , 1992 .

[7] Harald Niederreiter,et al. The serial test for congruential pseudorandom numbers generated by inversions , 1989 .

[8] Jürgen Lehn,et al. A non-linear congruential pseudo random number generator , 1986 .

[9] E. Wright,et al. An Introduction to the Theory of Numbers , 1939 .

[10] Rudolf Lide,et al. Finite fields , 1983 .

[11] Harald Niederreiter,et al. Recent trends in random number and random vector generation , 1991, Ann. Oper. Res..

[12] Harald Niederreiter. The serial test for pseudo-random numbers generated by the linear congruential method , 1985 .

[13] Harald Niederreiter,et al. Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.