Translation Laguerre Planes of Order 16

Translation Laguerre planes of order 16 are investigated, and a related search is carried out for translation ovals in the eight translation planes of order 16 and for certain collections of such ovals called 2-pencils. Although in some of these planes there are considerably more translation hyperovals through two infinite points than in the Desarguesian plane, such pencils only exist in the Desarguesian plane and in the Hall plane. From this we deduce that there are only two translation Laguerre planes of order 16, and that both are ovoidal over a translation oval.