  Using the method of asymptotic sum rules we estimated the size of $O(m_s
p_\pi^4)$ and $O(m_s^2 p_\pi^2)$ corrections to $\pi K$ scattering amplitude in
large $N_c$ limit. These corrections arise from the sixth order effective
chiral lagrangian (EChL). Our method enables us to estimate the corresponding
terms of the sixth order EChL in leading order of $1/N_c$ expansion in model
independent way. We found that the corrections numerically are suppressed in
spite of naive expectation of 30--35\%. Our estimation gives the value of these
corrections about 5--10\% .
