The existence of doubly resolvable \((v,3,2)\)-BIBDs (Q1899060)

The author shows that the necessary conditions for the existence of doubly resolvable \((v,3,2)\) balanced incomplete block designs, \(\text{DR} (v,3,2)\)-BIBDs, are also sufficient for \(v \geq 12\) with at most six possible exceptions. Specifically, such designs exist provided \(v \equiv 0 \pmod 3\), \(v \neq 6\), 9, except possibly for \(v \in \{72, 78, 90, 114, 117, 126\}\). Note that repeated blocks are allowed. Several direct and recursive constructions are employed.