On 6-sparse Steiner triple systems

AbstractWe give the first known examples of 6-sparse Steiner triple systems by constructing 29 such systems in the residue class 7 modulo 12, with orders ranging from 139 to 4447. We then present a recursive construction which establishes the existence of 6-sparse systems for an infinite set of orders. Observations are also made concerning existing construction methods for perfect Steiner triple systems, and we give a further example of such a system. This has order 135,859 and is only the fourteenth known. Finally, we present a uniform Steiner triple system of order 180,907