Secondary Index Generator

We introduce the motivation of the random number and analyze the quality characterization of the pseudorandom number generator. And we also introduce some familiar generators in this paper. The quadratic exponential method is one of the methods that generate pseudorandom number sequence. By this method, we provide two new pseudorandom generators over F_q, which are digital quadratic exponential pseudorandom numbers generator and quadratic exponential pseudorandom vectors generator. The distributions of the sequences generated by these generators are charactered by their star discrepancy or discrete discrepancy. The bound of the sequencs' one dimensional star discrepancy or discrete discrepancy is presented in this paper. The proofs are based on the estimate of certain character sum over F_q. If t is the period of the sequences, then the bound of the discrepancy is O(t^-1/4q^1/8+ε log q) for any ε> 0 when t≥q^1/2+2ε. It shows that the sequences are asymptotically uniformly distributed.