Let $X$ be an algebraic variety over field $k$ snd $n=\mathrm{dim}(X)$ .
We assume $X$ is unirational.
There exists $m \in \mathbb{N}$ and a dominant rational map $\phi : \mathbb{P}_k^m \dashrightarrow X$ by unirationality of $X$ , where $\mathbb{P}_k^m$ means $m$-dimensional projective space over $k$ .
Then $m \geq n$ holds.
My question
Can we construct a dominant rational map $\mathbb{P}_k^n \dashrightarrow X$ by using $\phi$ $??$