On \((351,126,45)\)-difference sets. (Q2715994)
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scientific article; zbMATH DE number 1600963
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \((351,126,45)\)-difference sets. |
scientific article; zbMATH DE number 1600963 |
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20 July 2005
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difference set
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On \((351,126,45)\)-difference sets. (English)
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The main result of this paper is that if an abelian group \(G\) contains a \((351,126,45)\)-difference set, then the exponent of \(G\) must be 39. This fills in two missing entries in the table of \textit{A. Vera López} and \textit{M. A. Garcia Sánchez} [J. Comb. Math. Comb. Comput. 23, 97-112 (1997; Zbl 0873.05020)] with a negative answer. Futhermore, it is shown that if a Spence difference set has the character divisibility property, then it is one of the difference sets constructed by \textit{E. Spence} [J. Comb. Theory, Ser. A 22, 103-106 (1977; Zbl 0357.05019)].
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