论文标题
与小$λ$的差异集
On difference sets with small $λ$
论文作者
论文摘要
在1989年的论文\ cite {arasu2}中，Arasu使用了对乘数的观察，以表明在任何Abelian组中都不存在$（352,27,2）$差异集。证明很短，不需要计算机帮助。我们表明，它可以应用于广泛的参数$（v，k，λ）$，特别是对于$λ$的小值。借助它，计算机搜索能够证明Prime Power的猜想是正确的，直至订购$ 2 \ cdot 10^{10} $，扩展了Hughes和Dickey的计算，以$λ= 2 $和$ K \ leq 5000 $最高$ 10^{10} $，并且在许多其他参数中表现出任何其他参数。
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 $(v,k,λ)$, particularly for small values of $λ$. 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 $λ=2$ and $k \leq 5000$ up to $10^{10}$, and show nonexistence for many other parameters.
