  We revisit the hardness of approximating the diameter of a network. In the
CONGEST model of distributed computing, $ \tilde \Omega (n) $ rounds are
necessary to compute the diameter [Frischknecht et al. SODA'12], where $ \tilde
\Omega (\cdot) $ hides polylogarithmic factors. Abboud et al. [DISC 2016]
extended this result to sparse graphs and, at a more fine-grained level, showed
that, for any integer $ 1 \leq \ell \leq \operatorname{polylog} (n) $,
distinguishing between networks of diameter $ 4 \ell + 2 $ and $ 6 \ell + 1 $
requires $ \tilde \Omega (n) $ rounds. We slightly tighten this result by
showing that even distinguishing between diameter $ 2 \ell + 1 $ and $ 3 \ell +
1 $ requires $ \tilde \Omega (n) $ rounds. The reduction of Abboud et al. is
inspired by recent conditional lower bounds in the RAM model, where the
orthogonal vectors problem plays a pivotal role. In our new lower bound, we
make the connection to orthogonal vectors explicit, leading to a conceptually
more streamlined exposition.
