  Let $X^n$ be a hypersurface in $\mathbb{P}^{n+1}$ with $n\geq 1$ defined over
a finite field $\mathbb{F}_q$ of $q$ elements. In this note, we classify, up to
projective equivalence, hypersurfaces $X^n$ as above which reach two elementary
upper bounds for the number of $\mathbb{F}_q$-points on $X^n$ which involve a
Thas' invariant.
