  Asymptotic net is an important concept in discrete differential geometry. In
this paper, we show that we can associate affine discrete geometric concepts to
an arbitrary non-degenerate asymptotic net. These concepts include discrete
affine area, mean curvature, normal and co-normal vector fields and cubic form,
and they are related by structural and compatibility equations. We consider
also the particular cases of affine minimal surfaces and affine spheres.
