A recursive method of construction of resolvable $BIB$-designs

A theorem is proved that every resolvable $BIB$-design $(v,k,\lambda)$ with $\lambda=k-1$ 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 $(v,k,\lambda)$ with $\lambda=k-1$ and $(v,k,\lambda)$ with $\lambda=(k-1)/2$