Existence of resolvable block designs

B. T. Rumov

Sbornik. Mathematics, Tome 28 (1976) no. 3, pp. 325-337

Résumé

A recursive method of constructing resolvable BIB designs (RBIB designs) using the existence of a special type of difference families is set forth. The existence of RBIB designs $(v,k,\lambda)$ whose parameters $k$ and $\lambda$ are connected by one of the relationships a) $\lambda=k-1$, b) $\lambda=(k-1)/2$, c) $\lambda=(k-1)/4$ or d) $\lambda=(k-1)/8$, as well as group-divisible resolvable designs in the group of RGD designs with parameters $(v,k,m,\lambda_1,\lambda_2)$, where $m=v/k$, $\lambda_1=\lambda$ and $\lambda_2=s\geq1$, is proved. Moreover, the existence of a RGD design ($vw,k,w,\lambda_1=0,\lambda_2=\lambda$) for given $w$ is derived from the existence of the RBIB design $(v,k,\lambda)$, and the existence of two series of $(v,k,\lambda)$-difference families with $\lambda=k/4$ and $\lambda=k/8$ is proved. Bibliography: 24 titles.