Simple 2-fold (3n,n,3) group divisible designs having a prescribed number of triples in common

In this note, we will give intersection numbers for two simple 2-fold (3n,n,3) group divisible designs (GDD). More precisely, we note that there exists two simple 2-fold (3n,n,3) GDDs which intersect in precisely k∈{0,1,2,…,2n2}\{2n2−1,2n2−2,2n2−3,2n2−5} triples for n⩾5. There are some exceptions for n=3,4.