On large partial ovoids of symplectic and Hermitian polar spaces

Abstract

In this paper we provide constructive lower bounds on the sizes of the largest partial ovoids of the symplectic polar spaces $\mathcal{W}(3,q)$, $q$ odd square, $q\not\equiv 0(\mathrm{mod}3)$, $\mathcal{W}(5,q)$ and of the Hermitian polar spaces $\mathcal{H}(4,q^2)$, $q$ even or $q$ odd square, $q\not\equiv 0(\mathrm{mod}3)$, $\mathcal{H}(6,q^2)$, $\mathcal{H}(8,q^2)$.