On generalized quasi-residual designs
Recall the following: If a (v,k,\(\lambda)\)-design D contains an s-fold block B, then \(b\geq sv\). In case of equality D is called a generalized symmetric design since then each block \(C\neq B\) meets B is \(y=k(k-1)/(v- 1)=\lambda /s\) points. Removing the points of B then results in a generalized residual design with parameters \(v'=v-k\), \(k'=k-y\), \(\lambda '=\lambda\). Any design D' having parameters of this type is called generalized quasi-residual. A (generalized) quasi-residual design is not necessarily (generalized) residual. Denote by SI(D') the smallest integer m such that the m-fold copy of the generalized quasi-residual design D' is actually generalized residual. \textit{V. C. Mavron}, \textit{R. C. Mullin} and \textit{A. Rosa} [J. Stat. Plann. Inference 10, 59-68 (1984; Zbl 0563.05012)] have proved that SI(D')\(\leq \left( \begin{matrix} k'+y\\ y\end{matrix} \right)\). The present authors improve this bound if D' is \(\alpha\)- resolvable and in case \(\lambda =2\). They also discuss some small examples.
scientific article; zbMATH DE number 4012621