On Ovoids of the Generalized Quadrangle $$H(3,q^2)$$

Abstract

We construct examples and families of locally Hermitian ovoids of the generalized quadrangle $$H(3,q^2)$$ . We also obtain a computer classification of all locally Hermitian ovoids of $$H(3,q^2)$$ for $$q \le 4$$ , and compare the obtained classification for $$q=3$$ with the classification of all ovoids of H(3, 9) which is also obtained by computer.