Existence conjecture for near triple arrays

Let $r$, $c$, and $v$ be positive integers. An $(r \times c, v)$-near triple array is an array with $r$ rows and $c$ columns on $v$ symbols satisfying the near triple array conditions defined in the paper.

Existence conjecture. $(r \times c, v)$-near triple arrays exist for any $c \geq r(r - 1)$ and $v \geq c$.

The paper establishes existence for $r=3$, $c \geq 6$, and $v \geq c$, while also proving nonexistence for certain parameters with $r \geq 4$. The conjecture proposes that the bound $c \geq r(r-1)$ suffices in general; its full status remains open.