  We determine a new set of parton distribution functions (ABMP16), the strong
coupling constant $\alpha_s$ and the quark masses $m_c$, $m_b$ and $m_t$ in a
global fit to next-to-next-to-leading order (NNLO) in QCD. The analysis uses
the $\overline{\mathrm{MS}}$ scheme for $\alpha_s$ and all quark masses and is
performed in the fixed-flavor number scheme for $n_f=3, 4, 5$. Essential new
elements of the fit are the combined data from HERA for inclusive
deep-inelastic scattering (DIS), data from the fixed-target experiments NOMAD
and CHORUS for neutrino-induced DIS, and data from Tevatron and the LHC for the
Drell-Yan process and the hadro-production of single-top and top-quark pairs.
The theory predictions include new improved approximations at NNLO for the
production of heavy quarks in DIS and for the hadro-production of single-top
quarks. The description of higher twist effects relevant beyond the leading
twist collinear factorization approximation is refined. At NNLO we obtain the
value $\alpha_s^{(n_f=5)}(M_Z) = 0.1147 \pm 0.0008$.
