Graham–Archdeacon conjecture on simple orderings of cyclic groups

Let $T\subseteq \mathbb{Z}_v\setminus\{0\}$. An ordering of the elements of $T$ is simple when its partial sums are all distinct and non-zero. Graham–Archdeacon conjecture. The set $T$ admits a simple ordering. This conjecture extends Graham's 1971 conjecture from cyclic groups of prime order to every cyclic group and implies Alspach's conjecture. It is known when $|T|\leq6$ and, by computer verification, for $v\leq25$; the general case remains open.