On A-optimal block matrices and weighing designs when N\(\equiv 3\,(mod\,4)\) (Q1099556)

Let \({\mathcal B}(N,n)\) denote the class of \(n\times n\) block matrices with \(B=(B_{ij})\) where \(B_{ij}=(N-3)I_{r_ i}+3J_{r_ i}\) and \(B_{ij}=-J_{r_ ir_ j}\) for \(i\neq j\), \(N\geq n\) and \(N\equiv 3 (mod 4)\). The A-optimal matrices in \({\mathcal B}(N,n)\) are classified. The relevance of this toward finding A-optimal weighing designs is explained.