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.
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