On the existence of pure \((v, 4, 3)\)-PMD
A PMD is a perfect cyclic design, introduced by \textit{N. S. Mendelsohn} in his article [Perfect cyclic designs, Discrete Math. 20(1977), 63-68 (1978; Zbl 0369.05015)], and later called a perfect Mendelsohn design. A \((v, k, \lambda)\)-PMD can be viewed as a \((v, k, \lambda(k- 1))\)-BIBD. The PMD is called pure if the underlying BIBD contains no repeated blocks. The author of the present article shows that a pure \((v, 4, 3)\)-PMD exists if and only if \(v\equiv 0\) or \(1\pmod 4\) and \(v\geq 8\).
scientific article; zbMATH DE number 906659