The hunt forweighing matrices of small orders

Abstract

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 ε (14; 18; 19; 21) and W(n,n - 1) for n ε (42; 46). We also discuss two possible approaches for constructing a W(66, 65), and show nonexistence of these under certain assumptions.