Steiner triple systems without parallel classes

Abstract

We construct Steiner triple systems without parallel classes for an infinite number of orders congruent to $3(\mathrm{mod}6)$. The only previously known examples have order $15$ or $21$.

5 pages, 0 figures. This version fixes a minor error in the journal version of the paper where we had neglected to say that two sum-zero triples must be removed before the additional triples in ${\mathcal{B}}^{\infty }\cup {\mathcal{B}}^{\ast }$ are added to create the Steiner triple system