  Let $n$ be a positive integer. In this paper we provide a general theory to
produce full orbit sequences in the affine $n$-dimensional space over a finite
field. For $n=1$ our construction covers the case of the Inversive Congruential
Generators (ICG). In addition, for $n>1$ we show that the sequences produced
using our construction are easier to compute than ICG sequences. Furthermore,
we prove that they have the same discrepancy bounds as the ones constructed
using the ICG.
