A Steiner quadruple system SQS(v) of order v is a family [formula omitted] of 4-element subsets of a v-element set V such that each 3-element subset of V is contained in precisely one B [formula omitted]. We prove that if T [formula omitted] B ≠ ø for all B [formula omitted] (i.e., if T is a transversal), then |T| ≥ v/2, and if T is a transversal of cardinality exactly v/2, then V \ T is a transversal as well (i.e., T is a blocking set). Also, in respect of the so-called ‘doubling construction’ that produces SQS(2v) from two copies of SQS(v), we give a necessary and sufficient condition for this operation to yield a Steiner quadruple system with blocking sets.
ASJC Scopus subject areas
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics