  Using Dumnicki's approach to showing non-specialty of linear systems
consisting of plane curves with prescribed multiplicities in sufficiently
general points on $\mathbb{P}^2$ we develop an asymptotic method to determine
lower bounds for Seshadri constants of general points on $\mathbb{P}^2$. With
this method we prove the lower bound 4/13 for 10 general points on
$\mathbb{P}^2$.
