In Theorem 6.1 of McSorley et al.  it was shown that, when v = r+c−1, every triple array TA(v, k, λrr, λcc, k : r × c) is a balanced grid BG(v, k, k : r×c). Here we prove the converse of this Theorem. Our final result is: Let v = r +c−1. Then every triple array is a TA(v, k, c−k, r−k, k : r × c) and every balanced grid is a BG(v, k, k : r × c), and they are equivalent.
McSorley, John P. "Double Arrays, Triple Arrays, and Balanced Grids with v = r + c - 1." (Nov 2005).