Further analysis of Peeling Sequences

Let $P\subset {\mathbb{R}}^2$ be a set of $n$ points in general position. A peeling sequence of $P$ is a list of its points, such that if we remove the points from $P$ in that order, we always remove the next point from the convex hull of the remainder of $P$. Using the methodology of Dumitrescu and Tóth \cite{Dumitrescu}, with a more careful analysis, we improve the upper bound on the minimum number of peeling sequences for an $n$ point set in the plane from ${12.29}^n\mathrm{/}100$ to ${9.78}^n\mathrm{/}500$.