Agrawal's conjecture on extremal triple arrays

Let $r$, $c$, and $d706_{cc}$ be parameters of a symmetric $2$-design on $r+c$ points, and suppose that $r-d706_{cc}>2$.

Agrawal's conjecture. If there is a symmetric $2$-$(r+c,r,d706_{cc})$ design with $r-d706_{cc}>2$, then there is an $(r\times c,r+c-1)$-triple array.

This conjecture asks whether Agrawal's construction from a symmetric design can always be completed from an unordered triple array to an ordered one under the stated condition. It remains open.