Classification of even-order ovoids in PG(3,q)

Determine all ovoids in the three-dimensional projective space PG(3, q) for even q.

Background

An ovoid in PG(3, q) is a set of q² + 1 points, for q not equal to 2, no three of which are collinear. In even characteristic, the known examples are elliptic quadrics and, for q of the form 2^2e+1, Tits ovoids; several small orders have been classified individually. The authors explicitly identify the determination of all even-order ovoids as unresolved.