This paper presents series of PBIB designs with m associate classes in which the treatment set is a subset of the Z(p m) -module of n × 1 vectors over the ring of integers modulo p m , p any prime. The association scheme of this series of designs is determined by the Fuller canonical form under row equivalence of n × 2 matrices [ a, b] for vectors a and b in the treatment set. The blocking procedure utilizes full rank s × n matrices over Z( p m ), 1 ⩽ s ⩽ n − 2, n ⩾ 3. For m = 2, n = 3, s =1 and for each prime p, each PBIB is regular divisible and yields a finite proper uniform projective Hjelmslev plane with parameters j = p and k = p( p + 1).