Irreducible symplectic varieties via K3-del Pezzo double covers

We construct a series of irreducible symplectic varieties of dimension $2n$, for $2\le n\le 10$, with second Betti numbers $16\le b_2\le 24$. They arise as non-trivial terminalisations of finite symplectic quotients of Beauville-Mukai systems on very general K3-del Pezzo double covers.