Products of involutions in symplectic groups over general fields (II)

Let s be an n-dimensional symplectic form over a field F of characteristic other than $2$, with $n>2$. In a previous article, we have proved that if F is infinite then every element of the symplectic group Sp(s) is the product of four involutions if n is a multiple of $4$ and of five involutions otherwise. Here, we adapt this result to all finite fields with characteristic not $2$, with the sole exception of the very special situation where $n=4$ and |F|=3, a special case which we study extensively.