  The problem on the construction of antisymmetric paramodular forms of
canonical weight 3 was open since 1998. Any cusp form of this type determines a
canonical differential form on any smooth compactification of the moduli space
of Kummer surfaces associated to $(1,t)$-polarised abelian surfaces. In this
paper, we construct the first infinite family of antisymmetric paramodular
forms of weight 3 as Borcherds products whose first Fourier-Jacobi coefficient
is a theta block.
