A Note on a Generating Set for \(N_5^\infty \)

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