GENERALIZED (T,S)-SEQUENCES, KRONECKER-TYPE SEQUENCES, AND DIOPHANTINE APPROXIMATIONS OF FORMAL LAURENT SERIES

The theory of (t, s)-sequences leads to powerful constructions of low- discrepancy sequences in an s-dimensional unit cube. We generalize thi s theory in order to cover arbitrary sequences constructed by the digi tal method and, in particular, the Kronecker-type sequences introduced by the second author. We define diophantine approximation constants f or formal Laurent series over finite fields and show their connection with the distribution properties of Kronecker-type sequences. The main results include probabilistic theorems on the distribution of sequenc es constructed by the digital method and on the diophantine approximat ion character of s-tuples of formal Laurent series over finite fields.