Improved upper bounds for the discrepancy of pairs of inversive congruential pseudorandom numbers with power of two modulus (Q1297757)

Inversive congruential pseudorandom numbers with a modulus which is a power of 2 were introduced by \textit{J. Eichenauer, J. Lehn}, and \textit{A. Topuzoǧlu} [Math. Comp. 51, 757-759 (1988; Zbl 0701.65008)]. An upper bound for the discrepancy of overlapping pairs of these pseudorandom numbers was established by the reviewer [Math. Comp. 52, 135-144 (1989; Zbl 0657.65007)], and for nonoverlapping pairs this was done by the author and the reviewer [Acta Arith. 65, 185-194 (1993; Zbl 0785.11043)]. In the present paper the author improves both of these upper bounds by making better use of the special structure of these sequences of pseudorandom numbers.