Eggs in finite projective spaces and unitals in translation planes

Inspired by the connection between ovoids and unitals arising from Buekenhout construction in André/Bruck-Bose representation of translation planes dimension at most two over their kernel, since eggs $$\textrm{PG}(4m-1,q)$$ , $$m\ge 1$$ are a generalization ovoids, we explore relation higher kernel. By investigating such relationship, construct unital Dickson semifield plane order $$3^{10}$$ which is represented $$\textrm{PG}(20,3)$$ cone whose base set points constructed dual Penttila-Williams egg $$\textrm{PG}(19,3)$$ . This not polar; so, up to knowledge authors, it seems be new plane.