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

Abstract

In Theorem 6.1 of McSorley et al. [3] it was shown that, when v=r+c?1, every triple array TA(v,k,?rr,?cc,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.