  In 1994, Alon construct a triangle-free $(n,d,\lambda)$-graph with $d =
\Omega(n^{2/3})$ and $\lambda = O(d^{1/2})$ for an exponentially increasing
sequence of integers $n$. Using his ingenious construction, we deduce that
there exist triangle-free $(n,d,\lambda)$-graphs with $d = \Omega(n^{2/3})$ and
$\lambda = O( (d \log n)^{1/2} )$ for all sufficiently large $n$.
