The Lang-Weil bounds imply that for a geometrically irreducible variety $X$ of dimension d over $\overline{\mathbb{F}_p}$ we have, $$|N_q(X)-q^{d}|\le O(q^{d-1/2}),$$

where $N_q(X)$ is the number of $\mathbb{F}_q$ points on $X$.

Are there any explicit expressions for what $O(q^{d-1/2})$ can be in general? I can find several references for the case of geometrically irreducible hypersurfaces (such as this question on math overflow). I just wanted a reference to a general explicit expression (I imagine I could calculate it from some inductive arguments, but I was wondering if there are known citable references).