On difference sets with small $\lambda$
| Autor: | Gordon, Daniel M. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In a 1989 paper \cite{arasu2}, Arasu used an observation about multipliers to show that no $(352,27,2)$ difference set exists in any abelian group. The proof is quite short and required no computer assistance. We show that it may be applied to a wide range of parameters $(v,k,\lambda)$, particularly for small values of $\lambda$. With it a computer search was able to show that the Prime Power Conjecture is true up to order $2 \cdot 10^{10}$, extend Hughes and Dickey's computations for $\lambda=2$ and $k \leq 5000$ up to $10^{10}$, and show nonexistence for many other parameters. Comment: 8 pages |
| Databáze: | arXiv |
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