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

On two upper bounds for hypersurfaces involving a Thas' invariant