  Let $\eta$ be a polarization with connected kernel on a superspecial abelian
variety $E^g$. We give a sufficient criterion which allows the computation of
the theta nullvalues of any quotient of $E^g$ by a maximal isotropic subgroup
scheme of $\ker(\eta)$ effectively. This criterion is satisfied in many
situations studied by Li and Oort. We used our method to implement an algorithm
that constructs supersingular curves of genus 3.
