Kirkman packing designs KPD\((\{3, 5^*\},v)\) (Q1611360)

A Kirkman packing design (KPD; also Kirkman school project design) \((\{3,s^{*}\},v)\) is a resolvable packing with maximum possible number of parallel classes, each class containing one block of size \(s\) and all others of size 3. The authors construct KPD\((\{3,5^{*}\},v)\) for all \(v \equiv 3\) (mod 3) with a few possible exceptions. The construction is recurrsive and uses some explicit small KPD and incomplete KPD.