Liftings of non-Singer difference sets to relative difference sets

Determine whether any difference sets other than those with parameters of complements of Singer difference sets admit liftings to relative difference sets for any value of the lifting parameter n.

Background

Relative difference sets can be obtained as liftings of ordinary difference sets. The paper explains that, apart from liftings associated with complements of classical Singer difference sets, no other nontrivial examples were known. This unresolved question concerns whether the known Singer-type constructions exhaust all possible cyclic relative difference-set liftings, without restricting the parameter n to a particular value.

The question is attributed to Pott and is presented as a broad existence problem motivating the computational searches conducted in the paper.