On 6-sparse Steiner triple systems |
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Authors: | AD Forbes TS Griggs |
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Institution: | Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom |
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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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Keywords: | Steiner triple system k-Sparse Steiner triple system Pasch configuration Mitre configuration Crown configuration Perfect Steiner triple system |
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