# 10

A Steiner quadruple system is an ordered pair $( V , B )$ where V is a finite set of symbols and B is a set of 4-element subsets of V called quadruples with the property that every 3-element subset of V is a subset of exactly one quadruple in B. |V| is called the order of the Steiner quadruple system. For short, we write SQS(v) to denote a Steiner quadruple system of order v.