Group divisible designs with block size four and two groups Original Research Article

We give some constructions of new infinite families of group divisible designs, GDDimage, including one which uses the existence of Bhaskar Rao designs. We show the necessary conditions are sufficient for image. For image there is one missing critical design. If image, then the necessary conditions are sufficient for image. For each of image, and 20 we indicate a small minimal set of critical designs which, if they exist, would allow construction of all possible designs for that n. The indices of each of these designs are also among those critical indices for every n in the same congruence class mod 12.