Existence conjecture for symmetric 0-ULSE coloured BIBDs

Let $v,k,\ell\in\mathbb{Z}^+$ satisfy the necessary parameter equation referred to in the source as Equation~, and suppose that there exists a symmetric BIBD on $v$ points with block size $k$. A $0$-ULSE $\ell$-coloured BIBD is a balanced incomplete block design with the stated zero-uniform locally semi-equitable colouring property. Existence conjecture for symmetric 0-ULSE coloured BIBDs. There exists a $0$-ULSE $\ell$-coloured symmetric BIBD on $v$ points with block size $k$. The authors report no counterexample and motivate the claim by their search, while the conjecture remains open.