# complexity of system of equations defining affine variety

Say you have an affine variety $$X$$ in $$n$$-dimensional affine space. (You can even assume we are over $$\mathbb{C}$$, but I believe the nature of my question is algebraic).

I want to bound from above the complexity of a system of equations defining $$X$$. My guess is that the following parameters should be enough:

1. $$n$$ - dimension of ambient space.

2. $$\mu$$ - dimension of $$X$$

3. $$d$$ - degree of $$X$$ in say the standart projective compactification of $$\mathbb{A}^n$$.

I don't mind what concept of complexity to take, say the max power in which any variable is taken from any equation.

Thank you very much!