Existence of small cyclic difference sets in four parameter cases

Determine whether cyclic difference sets exist for the parameter sets $(1561,105,7)$, $(2185,105,5)$, $(1111,111,11)$, and $(465,145,45)$.

Background

The paper states that cyclic difference sets are known for all parameters (v,k,λ)(v,k,\lambda) with k<105k<105, but identifies four smallest unresolved cases immediately beyond that range. These cases concern the existence of cyclic difference sets themselves, which serve as potential underlying objects for relative difference-set liftings.

Although the paper focuses primarily on liftings and circulant weighing matrices, the four parameter sets are explicitly recorded as open cases in its survey of known cyclic difference sets.

References

In particular, the existence of cyclic difference sets for all parameters $(v,k,\lambda)$ with $k < 105$ is known (the smallest open cases are $(1561,105,7)$, $(2185,105,5)$, $(1111,111,11)$ and $(465,145,45)$).

Cyclic relative difference sets and circulant weighing matrices  (2501.14924 - Gordon, 24 Jan 2025) in Section 2, Multipliers