On hyperovals of polar spaces

We derive lower and upper bounds for the size of a hyperoval of a finite polar space of rank 3. We give a computer-free proof for the uniqueness, up to isomorphism, of the hyperoval of size 126 of H(5, 4) and prove that the near hexagon ${\mathbb E_3}$ has up to isomorphism a unique full embedding into the dual polar space DH(5, 4).