A recursive method of construction of resolvable BIB-designs

A theorem is proved that every resolvable BIB-design (v,k,) with =k–1 and the parameters v and k such that there exists a set of k–1 pairwise orthogonal Latin squares of order v can be embedded in a resolvable BIB-design ((k+1)v, k, k–1). An analogous theorem is established for the class of arbitrary BIB-designs. As a consequence is deduced the existence of resolvable BIB-designs (v,k,) with =k–1 and =(k–1)/2.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 707–715, May, 1977.