Abstract
Balanced weighing matrices with parameters $$\left({1 + 18 \cdot {{{9^{m + 1}} - 1} \over 8},{9^{m + 1}},4 \cdot {9^m}} \right),$$ for each nonzero integer m are constructed. This is the first infinite class not belonging to those with classical parameters. It is shown that any balanced weighing matrix is equivalent to a five-class association scheme.
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