On Incomplete Group Divisible Designs

In this paper, we deal with recursive constructions for incomplete group divisible designs (IGDDs). Denoting \(GD[k,1,v; uv] – GD[k,1,n; un]\) by \((u,k)-IGD[v,n]\), we will prove, as an application, that a \((7,4)-IGD[v,n]\) exists if and only if \(v \geq 3n\) and \(\text{v – n} \equiv 0 \pmod{2}\).