Degree of polynomials in vanishing ideals of varieties.

Question

Let $\mathbb{V}\subseteq \mathbb{F}^n $ be a variety of dimension $r$ and degree $s$. What is the minimum/maximum degree of any polynomial in the vanishing ideal $\mathbb{I}(\mathbb{V})$ of $\mathbb{V}$? Are there any known lower or upper bounds on the degree of polynomials in $\mathbb{I}(\mathbb{V})$ in terms of $r$ and $s$?