Mixed group divisible designs with three groups and block size 4

A group divisible design (GDD) with three groups and block size 4 is called even, odd, or mixed if the sizes of the non-empty intersections of any of its blocks with any of the three groups are always even, always odd, or always mixed. It has been shown that the necessary conditions for the existence of GDDs of these three types are also sufficient except possibly for the minimal case of mixed designs for group size 5t5t (t>1t>1). In this paper, we complete the undetermined families of mixed GDDs using two constructions based on idempotent self-orthogonal Latin squares and skew Room squares.