  High dimensional entangled states have attracted much more attentions, due to
their strong nonlocality and much powerful capability for quantum information
processing. By the methods presented in this paper, arbitrary forms entangled
qudits including symmetric and asymmetric forms could be generated with the
weak cross-Kerr nonlinearity. These schemes are heralded by the detections of
single-photon detectors. If all the detectors do not register any single
photons, the generation is success with the probability $1/n^{M}$ determined by
dimension $n$ and partite $M$. Furthermore, these schemes work well even with
the common photon number nonresolving detectors, therefore they are feasible
with the current experimental technology.
