For a unipotent group G over a finite field, the theory of character sheaves allows us to relate the geometry of G to irreducible representations of G(Fq). In this talk, we define Lusztig-packets of representations and Lusztig-packets of character sheaves. In the case that G is connected, we give explicit relationships between character sheaves on G and irreducible characters of G(Fq) by using the sheaf-function correspondence. For certain G, this allows us to construct every irreducible character of G(Fq).