  In their 2009 note: \emph{Packing equal squares into a large square}, Chung
and Graham proved that the uncovered area of a large square of side length $x$
is $O\left(x^{(3+\sqrt{2})/7}\log x\right)$ after maximum number of
non-overlapping unit squares are packed into it, which improved the earlier
results of Erd\H{o}s-Graham, Roth-Vaughan, and Karabash-Soifer. Here we further
improve the result to $O(x^{5/8})$ that also helps to improve the bound for the
dual problem: finding the minimum number of unit squares needed for covering
the large square, from $x^2+O\left(x^{(3+\sqrt{2})/7}\log x\right)$ to
$x^2+O(x^{5/8})$.
