  We compute the medium-mass nuclei $^{16}$O and $^{40}$Ca using pionless
effective field theory (EFT) at next-to-leading order (NLO). The low-energy
coefficients of the EFT Hamiltonian are adjusted to experimantal data for
nuclei with mass numbers $A=2$ and $3$, or alternatively to results from
lattice quantum chromodynamics (QCD) at an unphysical pion mass of 806 MeV. The
EFT is implemented through a discrete variable representation in the harmonic
oscillator basis. This approach ensures rapid convergence with respect to the
size of the model space and facilitates the computation of medium-mass nuclei.
At NLO the nuclei $^{16}$O and $^{40}$Ca are bound with respect to decay into
alpha particles. Binding energies per nucleon are 9-10 MeV and 30-40 MeV at
pion masses of 140 MeV and 806 MeV, respectively.
