Blocking sets in \((v,\{ 2,4 \} ,1)\)-designs
A blocking set in a design is a partition of the points into two groups so that no block lies entirely within one class of the partition. In this paper, pairwise balanced designs on \(v\) points with block sizes two and four are considered. When \(v\equiv 1, 2\), or \(4\pmod{12}\), it is shown that such a PBD with a blocking set exists except possibly when \(v=37, 40\), or 73. When \(v\equiv 0, 3, 5, 6, 7, 8, 9, 11\pmod{12}\), it is shown that no such PBD has a blocking set. The situation when \(v\equiv 10\pmod{12}\) remains open.
scientific article; zbMATH DE number 993503