Motivated by the Beck-Fiala conjecture, we study discrepancy bounds for random sparse set systems. Concretely, these are set systems ( X ) , where each element x X lies in t randomly selected sets of , where t is an integer parameter. We provide new bounds in two regimes of parameters. We show that when X the hereditary discrepancy of ( X ) is with high probability O ( t log t ) ; and when X t the hereditary discrepancy of ( X ) is with high probability O (1) . The first bound combines the Lov{\'a}sz Local Lemma with a new argument based on partial matchings; the second follows from an analysis of the lattice spanned by sparse vectors.