Abstract
In this paper we consider the existence of 4-GDDs on v points with v≤50. We consider the case v≡1(mod3) and construct designs for all feasible group types here. We also enumerate all 4-GDDs with type 74 and compare the actions of their automorphism groups. When v≡0(mod3) and v≤50, there are no feasible group types for which existence has not been determined, but for v≡2(mod3) and v≤50, we obtain 4-GDDs for two more feasible group types.
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