The Hunt for Weighing Matrices of Small Orders

In this note we use a variety of techniques to construct new weighing matrices of small orders. In particular, we construct new examples of W(n, 9) for n ∈ { 14, 18, 19, 21} and W(n, n − 1) for n ∈ { 42, 46}. We also discuss two possible approaches for constructing a W(66, 65), and show nonexistence of these under certain assumptions.