  We propose a natural (2+1)-dimensional generalization of the Ablowitz-Ladik
lattice that is an integrable space discretization of the cubic nonlinear
Schroedinger (NLS) system in 1+1 dimensions. By further requiring rotational
symmetry of order 2 in the two-dimensional lattice, we identify an appropriate
change of dependent variables, which translates the (2+1)-dimensional
Ablowitz-Ladik lattice into a suitable space discretization of the
Davey-Stewartson system. The space-discrete Davey-Stewartson system has a Lax
pair and allows the complex conjugation reduction between two dependent
variables as in the continuous case. Moreover, it is ideally symmetric with
respect to space reflections. Using the Hirota bilinear method, we construct
some exact solutions such as multidromion solutions.
