Summary: The Maximum Diversity Problem (MDP) consists in selecting a subset \(M\) of given cardinality out of a set \(N\), in such a way that the sum of the pairwise diversities between the elements of \(M\) is maximum. New instances for this problem have been recently proposed in the literature and new algorithms are currently under study to solve them. As a reference for future research, this paper provides a collection of all best known results for the classical and the new instances, obtained by applying the state-of-the-art algorithms. Most of these results improve the published ones. In addition, the paper provides for the first time a collection of tight upper bounds, proving that some of these instances have been optimally solved. These bounds have been computed by a branch-and-bound algorithm based on a semidefinite formulation of the Quadratic Knapsack Problem (QKP), which is a generalization of the MDP.