Ovoids of the parabolic quadric Q(6, q) of \(\textrm{PG}(6,q)\) have been largely studied in the last 40 years. They can only occur if q is an odd prime power and there are two known families of ovoids of Q(6, q), the Thas-Kantor ovoids and the Ree-Tits ovoids, both for q a power of 3. It is well known that to any ovoid of Q(6, q) two polynomials \(f_1(X,Y,Z)\) , \(f_2(X,Y,Z)\) can be associated. In this paper we classify ovoids of Q(6, q) with \(\max \{\deg (f_1),\deg (f_2)\}<(\frac{1}{6.3}q)^{\frac{3}{13}}-1\) .
