A framework for constructing partial geometric difference sets

Partial geometric difference sets (PGDSs) were defined in Olmez (J Combin Des 22(6):252–269, 2014 ). They are used to construct partial geometric designs. We use the framework of extended building sets to find infinite families of PGDSs in abelian groups. Included in our new families of PGDSs are generalizations of the Hadamard, McFarland, Spence, Davis-Jedwab, and Chen difference sets.