A relation between constructive methods for Steiner trades and some block designs

In this paper, we attempt to construct some 3-way (v, k, 2) Steiner trades, specially for k = 5, by applying some block designs, such as BIBDs, RBs, GDDs, and RGDDs, specially GDDs. Also, we show the existence of a 3-way (v, 5, 1) Steiner trade for each volume s, s ≥12 except probably s ∈ {13, 14, 17, 19, 22, 23, 26, 29}.