The embedding in AG(3,q) of (0,2)-geometries containing a planar net

In De Clerck and Delanote (Design Codes Cryptogr. 32 (2004) 103-110), it is shown that if a (0,α)-geometry with α⩾3 is fully embedded in AG(n,q) then it is a linear representation. In this paper, we classify the (0,2)-geometries fully embedded in AG(3,q) such that there is at least one planar net. This result is a first and necessary step in the classification of (0,2)-geometries fully embedded in AG(n,q), which we complete in De Feyter (Adv. Geom., to appear).