Double Arrays, Triple Arrays and Balanced Grids with v=r+c - 1

In Theorem 6.1 of [3] 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.