Some more 5-GDDs, 4-frames and 4-RGDDs

In this paper, we continue to investigate the existence of 55-GDDs, 4-frames and 4-RGDDs, which have been studied by numerous researchers in the past two decades due to their vital applications in the constructions for other types of designs. Much progress has been made for the existence problems of these designs, while the problems are still open. Our new results mainly lie in the cases with relatively large group size. We also construct some smaller designs, including 44-RGDDs of types 21842184, 944944, 14101410, 18181818, 22102210 and 36113611.