Improving bounds for value sets of polynomials over finite fields

Let $\mathbb{F}_{q}$ be a finite field of characteristic $p$, and let $f \in \mathbb{F}_{q}[x]$ be a polynomial of degree $d > 0$. Denote the image set of this polynomial as $V_{f}=\{f(α)\midα\in\mathbb{F}_{q}\}$ and denote the cardinality of this set as $N_{f}$. A much sharper bound for $N_{f}$ i