Uniformly resolvable designs with index one, block sizes three and five and up to five parallel classes with blocks of size five
A \(\text{URD}(K;v)\) is a type of pairwise balanced design on \(v\) points with index 1 and block sizes from \(K\). Its blocks can be partitioned into parallel classes with all blocks in each parallel class of the same size. Necessary conditions for existence of a \(\text{URD}(\{3,5\};v)\) with \(r_5\) parallel classes of size 5 and \(r_3 = (v-1-4 r_5)/2\) parallel classes of size 3 are \(v \equiv 15 \pmod{30}\) and \(v \geq 45\). The author shows these conditions are sufficient for \(2 \leq r_5 \leq 5\), except possibly when \(r_5 = 3\), \(v = 105\) or \(r_5 \in \{2,4,5\}\), \(v=105, 165, 285, 345\).
scientific article; zbMATH DE number 5644961