7 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.

Ordering conjecture. For each parameter set in the family, at least some of these unordered triple arrays can be ordered to form triple arrays.

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 $U_T=U$.

A symmetric balanced incomplete block design (SBIBD) is a balanced incomplete block design with the same number of blocks as points; a triple array is the design introduced by Agra…

A triple array $T$ has column intersection size $4\lambda_{cc}$, and Construction associates arrays with Youden rectangles by deleting a column and its symbols and then exchanging…

Let $R(i)$ and $C(j)$ be the sets of letters assigned to row $i$ and column $j$, respectively, in the canonical construction with $v=r+c-1$ letters, and suppose that each cell…