  We construct skew corner-free sets in $[n]^2$ of size $n^{5/4}$, thereby
disproving a conjecture of Kevin Pratt. We also show that any skew corner-free
set in $\mathbb{F}_{q}^{n} \times \mathbb{F}_{q}^{n}$ must have size at most
$q^{(2-c)n}$, for some positive constant $c$ which depends on $q$.
