Embedding dimension of smooth affine variety of dimension $d$ , over an infinite perfect field, is $2d+1$?

Question

Let $k$ be an infinite perfect field.

Let $R$ be a finitely generated $k$-algebra of Krull dimension $d$ such that $R$ is regular.

Then is it true that there exists a surjective $k$-algebra homomorphism $k[x_1,\dots,x_{2d+1}]\to R $ ?