Properties C and D fail for Cₙʳ whenever n ≡ 2 4, n≥ 6 and r≥ 4

Let s(Cₙʳ) be the Erdős--Ginzburg--Ziv constant (zero-sums of length exactly n) and η(Cₙʳ) the short zero-sum constant. Properties C and D of Gao et al.\ assert that every sequence of the extremal length without the relevant zero-sums has the form Tⁿ⁻¹. For even n they imply s(Cₙʳ)=2ʳ(n-1)+1 and η(Cₙʳ)=(2ʳ-1)(n-1)+1. G.~Wang recently disproved both for C₆ʳ, r≥4. We prove that both fail for Cₙʳ for every n≡24 with n≥6 and every r≥4. More precisely, for these n we have: s(Cₙʳ)≥2ʳ(n-1)+2ʳ⁻²+1.