It was recently established that the Global Torelli theorem can be extended to irreducible symplectic orbifolds. This provides an important motivation in order to classify the different possible Beauville-Bogomolov lattices that can be found in this context. In the smooth case, few things were done for this purpose. However, we can mention the work of Guan that established that the second Betti number of a Hyperkahler fourfold is contained between 3 and 23. In this talk we will show that this result of Guan can be extended to primitively symplectic orbifolds and we will provide examples for several of the possible Betti numbers. This is a joint work in progress with Lie Fu.