of these systematic errors using effective field theory (EFT) methods, see, e.g. [@Bernard:2002yk]. With improved numerical algorithms and enlarged computing resources, we are entering a period where lattice data in conjunction with EFTs will provide physical predictions for QCD.

Another restriction in lattice simulations is the available momentum. With periodic boundary conditions, the momentum and hence momentum transfers are quantized. On current dynamical lattices the lowest non-zero momentum mode is $\sim 500 \, \texttt{MeV}$. Chiral EFTs predict the momentum transfer dependence of form factors. With current lattice sizes, however, the applicability of these theories to describe the momentum dependence is questionable. The restriction to quantized momentum transfer leads to a further impediment: the extraction of radii and moments that are only accessible in the near-forward limit is severely limited without *ad hoc* models for the momentum dependence. For a lattice of uniform spatial size $L$, periodic boundary conditions yield momentum modes $\bm{q} = 2 \pi \bm{n} / L$, for $\bm{n} \in \mathbb{Z}^3$. To reduce the momentum granularity one must increase the lattice volume and thus generate new gauge configurations—an extremely costly solution.[^1]

The use of periodic boundary conditions is one of simplicity not necessity. The quark fields need to periodic 