Abstract The problem of the construction of antisymmetric paramodular forms of canonical weight has been open since 1996. Any cusp form of this type determines a canonical differential form on any smooth compactification of the moduli space of Kummer surfaces associated to -polarised abelian surfaces. In this paper, we construct the first infinite family of antisymmetric paramodular forms of weight as automorphic Borcherds products whose first Fourier-Jacobi coefficient is a theta block. Bibliography: 32 titles.