  The asymptotic lattices and their transformations are studied within the line
geometry approach. It is shown that the discrete asymptotic nets are
represented by isotropic congruences in the Plucker quadric. On the basis of
the Lelieuvre-type representation of asymptotic lattices and of the discrete
analog of the Moutard transformation, it is constructed the discrete analog of
the W-congruences, which provide the Darboux-Backlund type transformation of
asymptotic lattices.The permutability theorems for the discrete Moutard
transformation and for the corresponding transformation of asymptotic lattices
are established as well. Moreover, it is proven that the discrete W-congruences
are represented by quadrilateral lattices in the quadric of Plucker. These
results generalize to a discrete level the classical line-geometric approach to
asymptotic nets and W-congruences, and incorporate the theory of asymptotic
lattices into more general theory of quadrilateral lattices and their
reductions.
