Stinson's strong starter conjecture for cyclic groups

Let $n\geq 5$ be an odd integer. A strong starter in the cyclic group $\mathbb{Z}_n$ is a starter satisfying the additional distinct nonzero pair-sum condition defined in the paper. Stinson's conjecture. There exists a strong starter in $\mathbb{Z}_n$ if and only if $n\neq 5,9$. The cases $n=5$ and $n=9$ are known exceptions, while existence was proved for every odd $n\neq 9$ with $7\leq n\leq 99$; the general cyclic case remains open.