I am working on the Davenport constant for groups, $D(G)$, which is the minimal number $d$ such that every sequence or multiset of $d$ elements of the group $G$ always contains some zero-sum subsequence.

For abelian groups, we know a lot of result and facts. In particular, $D(C_3^n)=1+2n$ so that maximal zero-sum free sequences have length $2n$. For example, the sequence consisting of each vector $e_i$ twice. Do we know exactly the structure of all maximal zero-sum free sequences?