Using the combinatorial patchworking, we construct an asymptotically maximal (in the sense of the generalized Harnack inequality) family of real algebraic hypersurfaces in an n-dimensional real projective space. This construction leads to a combinatorial asymptotic description of the Hodge numbers of algebraic hypersurfaces in the complex projective spaces and to asymptotically sharp upper bounds for the individual Betti numbers of primitive T-hypersurfaces in terms of Hodge numbers of the complexifications of these hypersurfaces.