  We consider two-component fermions with short-range interactions and large
scattering length. This system has universal properties that are realized in
several different fields of physics. In the limit of large fermion-fermion
scattering length $a_\mathrm{ff}$ and zero-range interaction, all properties of
the system scale proportionally with $a_\mathrm{ff}$. For the case with shallow
bound dimers, we calculate the dimer-dimer scattering phase shifts using
lattice effective field theory. We extract the universal dimer-dimer scattering
length $a_\mathrm{dd}/a_\mathrm{ff}=0.618(30)$ and effective range
$r_\mathrm{dd}/a_\mathrm{ff}=-0.431(48)$. This result for the effective range
is the first calculation with quantified and controlled systematic errors. We
also benchmark our methods by computing the fermion-dimer scattering parameters
and testing some predictions of conformal scaling of irrelevant operators near
the unitarity limit.
