A Note on a Generating Set for $N_5^{\mathrm{\infty }}$

Abstract

In this note, we construct a $(39,\{5,6,7\},1)$-PBD. Thus we have a finite generating set for the PBD-closed set $N_5^{\mathrm{\infty }}$ with at most three inessential elements, where $N_5^{\mathrm{\infty }}=\{1\}\cup \{v:v\ge 5\}$.