Group divisible designs with three groups and block size four (Q879385)

The more general notion of a group divisible design GDD\((n,m,k;\lambda_1,\lambda_2)\) is treated; this is a set of \(nm\) points partitioned into \(m\) groups each of size \(n\), together with a collection of \(k\)-subsets of points called blocks, so that every pair of points within a group appears in \(\lambda_1\) blocks and every pair between groups appears in \(\lambda_2\) blocks. The specific case when \(m=3\) and \(k=4\) is treated to obtain nearly complete results when \(n \in \{2,3,4,5\}\). Then under structural restrictions on intersections of blocks with groups, various classes of such designs are explored for larger group sizes.