Spanning Sets and Scattering Sets in Handcuffed Designs of order \(v\) and block size \(3\)

For each admissible \(v\) we exhibit a \(\mathrm{H}(v, 3, 1)\) with a spanning set of minimum cardinality and a \(\mathrm{H}(v, 3, 1)\) with a scattering set of maximum cardinality.