An Explicit Construction of Finite-Row Digital (0, S)-Sequences

In this paper we revisit the finite-row (0, s)-sequences as intro- duced by Hofer and Larcher, in particular those constructed by a scrambling of the Faure sequence. We give a simple explicit formula based on the Stirling num- bers (of the first kind) for the scrambling matrices. This explicit formula provides more insight into the (somewhat peculiar) recursively defined scrambling matrix used in the constructions of Hofer and Larcher and also into the correspond- ing finite-row generator matrices. It is then applied to the investigation of the self-similar structure of the generator matrices and to efficient generation of the sequence.