  For every constant $d \geq 3$ and $\epsilon > 0$, we give a deterministic
$\mathrm{poly}(n)$-time algorithm that outputs a $d$-regular graph on
$\Theta(n)$ vertices that is $\epsilon$-near-Ramanujan; i.e., its eigenvalues
are bounded in magnitude by $2\sqrt{d-1} + \epsilon$ (excluding the single
trivial eigenvalue of~$d$).
