Some non-existence results for distance-$j$ ovoids in small generalized   polygons
  We give a computer-based proof for the non-existence of distance-$2$ ovoids in the dual split Cayley hexagon $\mathsf{H}(4)^D$.   Furthermore, we give upper bounds on partial distance-$2$ ovoids of $\mathsf{H}(q)^D$ for $q \in \{2, 4\}$. 
Anurag Bishnoi and Ferdinand Ihringer
math.CO