A projective plane of order 16

A projective plane of order 16 is constructed. It is a translation plane and appears to be new. The representation of the collineation group on the axis of the plane has a normal subgroup isomorphic to L₃ (2) with factor group isomorphic to S₃. The orbits of this representation have lengths 14 and 3. If two points in the latter orbit are chosen to define a sharply doubly transitive set of permutations, the permutations from the multiplicative loop generate a group isomorphic to A₇. The plane is of Lenz-Barlotti class IVa.1.