Constructions of doubly resolvable Steiner quadruple systems
A Steiner quadruple system (SQS\((v)\)) is a design with block size 4 in which every set of three points lies in exactly one block. This paper gives two general constructions for doubly resolvable SQS\((v)\)s; one obtains a doubly resolvable SQS\((2v)\) from a doubly resolvable SQS\((v)\), and the other makes use of doubly resolvable candelabra quadruple systems. Using these, doubly resolvable SQS\((v)\)s are obtained for \(m \in \{1,5,7,11,17,26\}\) and \(n\) a positive integer, whenever $v$ is of one of the following forms: $m \cdot 2^n$ with $n \geq 2$, $(m,n) \neq (1,3)$, and $(3m \cdot 2^n) - 16$ with $n \geq 4$, $(m,n) \neq (1,5)$.
scientific article; zbMATH DE number 7346955
scientific article