The asymptotic existence of BIBDs having a nesting

Xinyue Ming, Tao Feng, Menglong Zhang

A $(v,k,\lambda )$-BIBD $(X,\mathcal{B})$ can be nested if there is a mapping $\varphi :\mathcal{B}\to X$ such that $(X,\{B\cup \{\varphi (B)\}\mid B\in \mathcal{B}\})$ is a $(v,k+1,\lambda +1)$-packing. A…