Odd and even group divisible designs with two groups and block size four Original Research Article

We show the necessary conditions are sufficient for the existence of GDD(n,2,4; λ1, λ2) with two groups and block size four in which every block intersects each group exactly twice (even GDDʹs) or in which every block intersects each group in one or three points (odd GDDʹs). We give a construction for near 3-resolvable triple systems TS(n,3,6) for every n⩾4, and these are used to provide constructions for several families of GDDs.