On Kirkman packing designs KPD\((\{3,4\},v)\). (Q1428517)

A Kirkman packing design KPD\((\{{3,4^{\ast \ast }\}},v)\) is a collection of the maximum possible number of parallel classes (= partitions of the underlying set \(V\), \(\left| V\right| =v\)) so that each parallel class consists of two blocks of size 4, and \((v-8)/3\) blocks of size 3, and each pair of elements from \(V\) occurs in at most one block. The authors prove that for each \(v\geq 32,\) \(v\equiv 2\pmod 3\) there is a KPD\((\{{ 3,4^{\ast \ast }\}},v)\) and contains \(\left\lfloor \frac{v-5}{2} \right\rfloor \) parallel classes.