On pseudorandom [0,1) and binary sequences

This paper studies links between uniform pseudorandom sequences of real numbers in [0, 1) and pseudorandom binary sequences. It is proved that good pseudorandom [0, 1) sequences induce binary sequences that have small correlation and well-distribution measures. On the other hand, given a binary sequence with small combined well-distribution-correlation measure, it is shown how to construct a [0, 1) sequence with small discrepancy. The special cases of linear congruential pseudorandom sequences and of Legendre symbol sequences are analyzed in more detail.