Let $R = k[x_1 , \ldots , x_n]$ be the polynomial ring with $n$ variables where $k$ is a field. Let $I = \langle f_1, \ldots , f_t \rangle$ be an ideal of $R$ with $t$ generators. By Hilbert Syzygy Theorem, we know that $\text{pdim } I \leq n$.
Is there a relation between $t$ and $\text{pdim } I$? Can we say that $\text{pdim } I \leq t$? or can we say that $\text{pdim } R/I \leq t$?