We present a variant of a universality result of R\"odl [On universality of graphs with uniformly distributed edges, Discrete Math. 59 (1986), no. 1-2, 125-134] for sparse, $3$-uniform hypergraphs contained in strongly jumbled hypergraphs. One of the ingredients of our proof is a counting lemma for fixed hypergraphs in sparse ``pseudorandom'' uniform hypergraphs, which is proved in the companion paper [Counting results for sparse pseudorandom hypergraphs I].
['Yoshiharu Kohayakawa', 'G. O. Mota', 'Mathias Schacht', 'Anusch Taraz']
Counting results for sparse pseudorandom hypergraphs II