On opposite orthogonal Steiner triple systems of non-prime-power order (Q1613498)
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scientific article; zbMATH DE number 1792426
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On opposite orthogonal Steiner triple systems of non-prime-power order |
scientific article; zbMATH DE number 1792426 |
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On opposite orthogonal Steiner triple systems of non-prime-power order (English)
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29 August 2002
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The opposite of Steiner triple systems (STS) developed from a Steiner difference family in an additive abelian group is formed by taking the negative of each triple (elementwise). It is noted that an infinite family of non-prime-power orders do not admit STS skew-orthogonal to their opposites. However, computational methods easily find STS orthogonal to their opposites in cyclic groups of all \(1\pmod 6\) orders \(n< 1000\), \(n\neq 25\). In particular, this settles the results of a search for order 55 mentioned in an earlier paper of Schreiber.
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hill climbing
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Steiner triple systems
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skew-orthogonal
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