Group divisible designs with block size 4 and group sizes 4 and 7

In this paper, we consider the existence of group divisible designs (GDDs) with block size $4$ and group sizes $4$ and $7$. We show that there exists a 4-GDD of type $4^t 7^s$ for all but a finite specified set of feasible values for $(t, s)$.Comment: arXiv admin note: substantial text overlap with arXiv:2109.1122