Eggs in finite projective spaces and unitals in translation planes

Inspired by the connection between ovoids and unitals arising from the Buekenhout construction in the Andre/Bruck-Bose representation of translation planes of dimension at most two over their kernel, and since eggs of PG(4m - 1, q), m >= 1, are a generalization of ovoids, we explore the relation between eggs and unitals in translation planes of higher dimension over their kernel. By investigating such a relationship, we construct a unital in the Dickson semifield plane of order 310, which is represented in PG(20, 3) by a cone whose base is a set of points constructed from the dual of the Penttila-Williams egg in PG(19, 3). This unital is not polar; so, up to the knowledge of the authors, it seems to be a new unital in such a plane.