3 problems

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.

Existence conjecture. For any prime power $q$, there is a $\left(\frac{q^3-1}{q-1},\frac{q^4-1}{q-1},\frac{(q^4-1)(q^3-1)}{(q^2-1)(q-1)}\right)$-triple array.

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 $U_T=U$.