  We reconstruct $f(T)$ theories from three different holographic dark energy
models in different time durations. For the HDE model, the dark energy
dominated era with new setting up is chosen for reconstruction, and the
radiation dominated era is chosen when the involved model changes into NADE.
For the RDE model, radiation, matter and dark energy dominated time durations
are all investigated. We also investigate the limitation which prevents an
arbitrary choice of the time duration for reconstruction in HDE and NADE, and
find that an improved boundary condition is needed for a more precise
reconstruction of $f(T)$ theory.
