A special class of nested Steiner triple systems (Q1917506)

A nested Steiner triple system of order \(v\), \(\text{NSTS}(v)\), is an \(\text{STS}(v)\) with a point added to each block in such a way that the resulting blocks form a 2-\((v, 4, 2)\) design. The author defines a partitionable nested triple system to be an \(\text{NSTS}(v)\) whose blocks can be partitioned into two 2-\((v, 4, 1)\) designs. He proves, by construction, that a partitionable \(\text{NSTS}(v)\) exists iff \(v\equiv 1\pmod{12}\). The general construction uses group divisible designs and special cases are dealt with by ad hoc constructions.