  We study algorithms for estimating the size of maximum matching. This problem
has been subject to extensive research. For $n$-vertex graphs, Bhattacharya,
Kiss, and Saranurak [FOCS'23] (BKS) showed that an estimate that is within
$\varepsilon n$ of the optimal solution can be achieved in
$n^{2-\Omega_\varepsilon(1)}$ time, where $n$ is the number of vertices. While
this is subquadratic in $n$ for any fixed $\varepsilon > 0$, it gets closer and
closer to the trivial $\Theta(n^2)$ time algorithm that reads the entire input
as $\varepsilon$ is made smaller and smaller.
  In this work, we close this gap and show that the algorithm of BKS is close
to optimal. In particular, we prove that for any fixed $\delta > 0$, there is
another fixed $\varepsilon = \varepsilon(\delta) > 0$ such that estimating the
size of maximum matching within an additive error of $\varepsilon n$ requires
$\Omega(n^{2-\delta})$ time in the adjacency list model.
