Generating sets in Steiner triple systems (Q2777505)

Let \(W\) be a subset of the point set \(V\) of a Steiner triple system (STS). The set \(W\) is a \(k\)-generating set, if in the Steiner quasigroup associated with the STS, every element of \(V\) can be written as a product of at most \(k\) elements of \(W\). When \(k=2\) such a generating set is a spanning or dominating set, and these have been applied in constructions of STS with complete arcs. The authors study the case \(k=3\) under the condition that every element of \(V\setminus W\) can be written in exactly one way as a product of at most 3 elements of \(W\).