1. On 6-sparse Steiner triple systems
- Author
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Forbes, A.D., Grannell, M.J., and Griggs, T.S.
- Subjects
- *
STEINER systems , *BLOCK designs , *CONSTRUCTION , *COMBINATORICS - Abstract
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. [Copyright &y& Elsevier]
- Published
- 2007
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