Algorithmic construction of simultaneous number system in the lattice of Gaussian integers

Abstract. In [1] number system constructions were analysed using general block diagonal bases. As a special case simultaneous systems were considered in the lattice of Gaussian integers. Extending the result of G. Nagy [2] it was proved that except 43 cases, the Gaussian integers can always serve as basic blocks for simultaneous number systems using dense digit sets. In this paper we analyze the remaining cases and we give a complete solution for the problem.