Transitive hyperovals in finite projective planes

Let $\Omega$ be a hyperoval in a projective plane $\pi$ of even order $n$, and $G$ the collineation group of $\pi$ preserving $\Omega$. If $G$ acts transitively on the points of $\Omega$, then $\Omega$ is a transitive hyperoval. By a deep result due to M. Biliotti and G. Korchm\'{a}ros (1987), if $\Omega$ is transitive and $|G|$ is divisible by $4$, then either $n=2,4$ and $\Omega$ is a hyperconic, or $n=16$ and $|G|\leq 144$. In this paper, it is shown that the case $n=16$ with $|G|=144$ only occurs when $\pi\cong\mathrm{PG}(2,16)$ and $\Omega$ is the Lunelli-Sce-Hall hyperoval.