Every symplectic spread of PG(3, q), or equivalently every ovoid of Q(4, q), is shown to give a certain family of permutation polynomials of GF(q) and vice-versa. This leads to an algebraic proof of the existence of the Tits-L¨uneburg spread of W(22h+1) and the Ree-Tits spread of W(32h+1), as well as to a new family of low-degree permutation polynomials over GF(32h+1).
Ball, S.; Zieve, M. Symplectic spreads and permutation polynomials. A: International Conference on Finite Fields and Applications. "Finite Fields and Applications". Toulouse: Springer, 2004, p. 79-88.