Lachaud's point-count bound for large-dimensional complete intersections

Let $X\subset\mathbb{P}^{n}$ be a projective algebraic set defined over $\mathbb{F}_{q}$, of dimension $m\geq n/2$ and degree $d\leq q+1$, which is an i.t. complete intersection. Writing $\pi_j=|\mathbb{P}^{j}(\mathbb{F}_q)|$, Lachaud's conjecture.

$$|X(\mathbb{F}_{q})|\leq d\pi_m-(d-1)\pi_{2m-n}=d(\pi_m-\pi_{2m-n})+\pi_{2m-n}.$$

This bound was proposed for point counts of projective complete intersections in the small-codimension range. The source states that the conjecture has been proved by Couvreur.