Noether number inequality for all finite groups

Establish whether, for every finite group G, the inequality d(G) + 1 ≤ β(G) holds, where d(G) denotes the small Davenport constant and β(G) denotes the Noether number of G.

Background

The paper discusses connections between the Davenport constants and invariant theory. For abelian groups, Schmid proved the equality d(G) + 1 = β(G). Cziszter and Domokos extended this by proving d(G) + 1 ≤ β(G) for groups having a cyclic subgroup of index 2. The authors point out that it remains unresolved whether this inequality extends to all finite groups.

This question ties the combinatorial invariant d(G) to the invariant-theoretic quantity β(G) and seeks a general principle valid across all finite groups.