Professor Jones aims to devise a matrix multiplication algorithm surpassing Strassen's algorithm in asymptotic efficiency. His method employs a divide$-$and$-$conquer approach, segmenting matrices into $(2/4)\backslash$times $(1/4)$ pieces, with the divide and combine steps collectively consuming $($n$^2)$ time. To ascertain the number of subproblems necessary for superiority over Strassen's algorithm, the recurrence for the running time T$($n$)$ conforms to T$($n$)=$ aT $(1/4)+($n$^2)$ when his algorithm generates a subproblems. What's the largest integer value of a that ensures Professor Jones's algorithm outperforms Strassen's algorithm asymptotically?