  We present the scheme-invariant unpolarized and polarized flavor non-singlet
evolution equation to N$^3$LO for the structure functions $F_2(x,Q^2)$ and
$g_1(x,Q^2)$ including the charm- and bottom quark effects in the asymptotic
representation. The corresponding evolution is based on the experimental
measurement of the non-singlet structure functions at a starting scale $Q_0^2$.
In this way the evolution does only depend on the strong coupling constant
$\alpha_s(M_Z)$ or the QCD scale $\Lambda_{\rm QCD}$ and the charm and bottom
quark masses $m_c$ and $m_b$ and provides one of the cleanest ways to measure
the strong coupling constant in future high luminosity deep-inelastic
scattering experiments. The yet unknown parts of the 4-loop anomalous
dimensions introduce only a marginal error in this analysis.
