Existence conjecture for type 2 cyclic Legendre difference families

Let $(X,Y)$ be a Legendre difference family in the cyclic group ${\mathbb Z}_v$. It is of type $2$ when neither block is a difference set; equivalently, if one block is a difference set then both are, and the family is of type $1$.

Type 2 existence conjecture. Legendre difference families of type $2$ exist for all odd lengths $v>8$.

This is presented as a stronger version of the conjecture that cyclic Legendre difference families exist for every odd length $v>2$. The constructions in the paper concern new lengths $91$, $93$, and $123$, while the asserted all-length type $2$ existence remains open.