Geography of simply connected spin symplectic 4-manifolds

We present an algorithm that produces new families of closed simply connected spin symplectic 4-manifolds with nonnegative signature that are interesting with respect to the symplectic geography problem. In particular, for each odd integer q satisfying q ≥275, we construct infinitely many pairwise nondiffeomorphic irreducible smooth structures on the topological 4-manifold q(S² × S²), the connected sum of q copies of S ² × S².