  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.
