Type-D solutions of the Einstein and Born-Infeld nonlinear electrodynamics equations

All type-D solutions of the Einstein-Born-Infeld equations for an algebrically general nonlinear electromagnetic field aligned along the Debever-Penrose directions are determined. The most general classes of solutions are nonlinear electromagnetic generalizations of the NUT-B-tilde(+) and anti-NUT-B-tilde(-) metrics. Subfamilies of solutions are the generalized Reissner-Nordstrom and anti-Reissner-Nordstrom metrics. The most special solution is the Bertotti-Robinson metric interpreted from the viewpoint of nonlinear electrodynamics