On 6-sparse Steiner triple systems

Forbes, A.D.; Grannell, M.J. and Griggs, T.S. (2007). On 6-sparse Steiner triple systems. Journal of Combinatorial Theory, Series A, 114(2) pp. 235–252.

DOI: https://doi.org/10.1016/j.jcta.2006.04.003

URL: http://mcs.open.ac.uk/mjg47/Papers/sixsparsea.pdf

Abstract

We 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.

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