Agrawal's ordering conjecture for extremal unordered triple arrays

Let $U$ be an $(r\times c,r+c-1)$-unordered triple array, let $e$ denote its mixed intersection parameter, and assume $e>2$. An ordered triple array $T$ has underlying unordered triple array $U_T$.

Agrawal's ordering conjecture. For any $(r\times c,r+c-1)$-unordered triple array $U$ with $e>2$, there is an $(r\times c,r+c-1)$-triple array $T$ with $U_T=U$.

This strengthens Agrawal's existence conjecture by requiring every eligible unordered triple array to be orderable. The paper states that it remains open, with computational evidence and special cases discussed later.