Given the polynomial space $\Pi_d^n$ which contains all the d-variable polynomials of degree up to $n$ and some scattered points $X\subset \Omega\subset\mathbb{R}^d$ ($\Omega$ is an open subset).

Since $\Pi_d^n$ is finite dimensional space there must be a constant $C$ such that

$ \left\|p\right\|_{l_2(X)}\leq C\left\|p\right\|_{L_2} $ for all $p\in\Pi_d^n$

where $\left\|p\right\|^2_{l_2(X)} = \frac{1}{|X|}\sum_{x\in X} p(x)^2$ and $\left\|p\right\|^2_{L_2} = \int_{\Omega} p(x)^2dx$.

Is it possible to find the constant $C$? Or at least gauge some understanding into how $C$ depends on $\Omega$, $X$, $n$ and $d$?

Thanks.