Published in Designs, Codes, and Cryptography, 37(2), 313-318. The original publication is available at


In Theorem 6.1 of McSorley et al. [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, ck, rk, k : r × c) and every balanced grid is a BG(v, k, k : r × c), and they are equivalent.

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