Sequences in abelian groups G of odd order without zero-sum subsequences of length exp(G)

We present a new construction for sequences in the finite abelian group without zero-sum subsequences of length n, for odd n. This construction improves the maximal known cardinality of such sequences for r > 4 and leads to simpler examples for r > 2. Moreover we explore a link to ternary affine caps and prove that the size of the second largest complete caps in AG(5, 3) is 42.