A characterization of special Laguerre planes and extended dual affine planes
The author proves the following theorem: Let \(\rho\) be a nondegenerate finite connected incidence structure. Let the residue of each point be a dual affine plane. Then either \(\rho\) is an extended dual affine plane or \(\rho\) is a special Laguerre plane. Here an extended dual plane is an incidence structure such that the residue of each point is a dual affine plane, and each pair of points os in at least one block. (Finite extended dual affine planes exist only of order 2,4 and (dubiously) 10). A special Laguerre plane is a nondegenerate transversal 3-design such that the residue of each point is a dual affine plane. Special Laguerre planes are equivalent to certain codes.
scientific article; zbMATH DE number 3876066