In a 1989 paper, Arasu (Arch Math 53:622–624, 1989) 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 \(k \le 5000\) up to \(10^{10}\), and show nonexistence for many other parameters.

在1989年的一篇论文中，Arasu（Arch Math 53：622–624，1989）使用有关乘数的观察结果表明，在任何阿贝尔群中都没有（352，27，2）差异集。证明很短，不需要计算机协助。我们证明它可以应用于广泛的参数\（（v，k，\ lambda）\），尤其是对于\（\ lambda \）的较小值。有了它，计算机搜索就能够证明素数幂猜想在\（2 \ cdot 10 ^ {10} \）阶下是正确的，扩展了Hughes和Dickey对\（\ lambda = 2 \）和\（ k \ le 5000 \）到\（10 ^ {10} \）为止，并显示许多其他参数不存在。