On 6-sparse Steiner triple systems

Authors:
A. D. Forbes;M. J. Grannell;T. S. Griggs
Affiliations:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom;Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom;Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom
Venue:
Journal of Combinatorial Theory Series A
Year:
2007

Citing 0
Cited 2

Nonexistence of sparse triple systems over abelian groups and involutions

Journal of Algebraic Combinatorics: An International Journal
The existence of 5-sparse Steiner triple systems of order n ≡3mod6, n∉{9,15}

Journal of Combinatorial Theory Series A

Quantified Score

Hi-index	0.01

Visualization

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.