Simple 2-fold group divisible designs having a prescribed number of triples in common

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