  We present extractions of the nucleon non-singlet moments utilizing new
precision data on the deuteron $F_2$ structure function at large Bjorken-$x$
determined via the Rosenbluth separation technique at Jefferson Lab
Experimental Hall C. These new data are combined with a complementary set of
data on the proton previously measured in Hall C at similar kinematics and
world data sets on the proton and deuteron at lower $x$ measured at SLAC and
CERN. The new Jefferson Lab data provide coverage of the upper third of the $x$
range, crucial for precision determination of the higher moments. In contrast
to previous extractions, these moments have been corrected for nuclear effects
in the deuteron using a new global fit to the deuteron and proton data. The
obtained experimental moments represent an order of magnitude improvement in
precision over previous extractions using high $x$ data. Moreover, recent
exciting developments in Lattice QCD calculations provide a first ever
comparison of these new experimental results with calculations of moments
carried out at the physical pion mass, as well as a new approach which first
calculates the quark distributions directly before determining moments.
