The known maximal partial ovoids of size $q^2-1$ of Q(4,q)
  We present a description of maximal partial ovoids of size $q^2-1$ of the parabolic quadric $\q(4,q)$ as sharply transitive subsets of $\SL(2,q)$ and show their connection with spread sets. This representation leads to an elegant explicit description of all known examples. We also give an alternative representation of these examples which is related to root systems. 
Kris Coolsaet, Jan De Beule and Alessandro Siciliano
math.CO