Symplectic translation planes and line ovals

A symplectic spread of a 2n-dimensional vector space V over GF(q) is a set of q(n) + 1 totally isotropic n-subspaces inducing a partition of the points of the underlying projective space. The corresponding translation plane is called symplectic. We prove that a translation plane of even order is symplectic if and only if it admits a completely regular line oval. Also, a geometric characterization of completely regular line ovals, related to certain symmetric designs Y-1(2d), is given. These results give a complete solution to a problem set by W. M. Kantor in apparently different situations.