  In this paper we start by briefly surveying the theory of Fractional Jumps
and transitive projective maps. Then, we give an efficient construction of a
fractional jump of a projective map and we extend the compound generator
construction for the Inversive Congruential Generator to Fractional jump
sequences. In addition, we provide new results on the absolute jump index, on
projectively primitive polynomials, and on the explicit description of
fractional jump generators.
