Sets of Type (d1, d2) in projective Hjelmslev planes over Galois Rings

In this paper we construct sets of type (d1, d2) in the projective Hjelmslev plane. For computational purposes we restrict ourself to planes over Zps with p a prime and s> 1, but the method is described over general Galois rings. The existence of sets of type (d1, d2) is equivalent to the existence of a solution of a Diophantine system of linear equations. To construct these sets we prescribe automorphisms, which allows to reduce the Diophantine system to a feasible size. At least two of the newly constructed sets are ’good’ u−arcs. The size of one of them is close to the known upper bound