Homogeneous Interpolation and Some Continued Fractions

We prove: if $d\mathrm{/}m<2280\mathrm{/}721$, there is no curve of degree $d$ passing through $n=10$ general points with multiplicity $m$ in ${\mathbf{P}}^{\mathbf{2}}$. Similar results are given for other special values of $n$. Our bounds can be naturally written as certain palindromic continued fractions.