  We present a determination of the strong coupling constant and heavy quark
masses in (2+1)-flavor QCD using lattice calculations of the moments of the
pseudo-scalar quarkonium correlators at several values of the heavy valence
quark mass with Highly Improved Staggered Quark (HISQ) action. We determine the
strong coupling constant in the $\overline{MS}$ scheme at four low-energy
scales corresponding to $m_c$, $1.5m_c$, $2m_c$, and $3m_c$, with $m_c$ being
the charm quark mass. The novel feature of our analysis that up to eleven
lattice spacings are used in the continuum extrapolations, with the smallest
lattice spacing being $0.025$ fm. We obtain
$\Lambda_{\overline{MS}}^{n_f=3}=298 \pm 16$ MeV, which is equivalent to
$\alpha_s(\mu=M_Z,n_f=5)=0.1159(12)$. For the charm and bottom quark masses in
the $\overline{MS}$ scheme, we obtain: $m_c(\mu=m_c,n_f=4)=1.265(10)$ GeV and
$m_b(\mu=m_b,n_f=5)=4.188(37)$ GeV.
