Some new group divisible designs with block size 4 and two or three group sizes

Group divisible designs (GDDs) with block size 4 and at most 30 points are known for all feasible group types except three, namely 2354,3562, and 2255. In this paper we provide solutions for the first two of these three 4-GDDs without assuming any automorphisms. We also construct several other 4-GDDs. These include classes of 4-GDDs of types (3m)4(6m)q(3n)1 for 0 <= n <=(q+1)m where q is an element of{2,3} and solutions for 4-GDDs of types 3t6s for a wide range of values of s >= 2,t >= 4 satisfying t equivalent to 0 or 1(mod4), including all cases with 4 <= t <= s-1. Most of the remaining unknown 4-GDDs of type 3t6s have (s-1)<t<2(s-1).