  Ion-ion collisions at relativistic energies have been shown recently to be a
promising technique for the production of hypernuclei. In this article, we
further investigate the production of light $\Lambda$ hypernuclei by use of a
hybrid dynamical model, cascade-coalescence followed by Fermi breakup. The
predictions are then compared with the available experimental data. The
dependence of the production cross section upon the beam energy, beam mass
number as well as different projectile-target combinations is investigated. In
particular, we evaluate the yields and signal-over-background ratio in the
invariant-mass spectrum for carbon projectiles impinging on hydrogen and carbon
targets and various coincidence conditions in the experiment using the
theoretical calculation as an input. It is found that comparing with carbon
target, hydrogen target also leads to sizable hypernuclear yields, even for
exotic species, and the hydrogen target could improve significantly
signal-over-background ratio in some hypernuclear invariant mass studies.
