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.

中文翻译：

---

一族平衡的广义加权矩阵

带参数的平衡称重矩阵

$$\left({1 + 18 \cdot {{{9^{m + 1}} - 1} \超过 8},{9^{m + 1}},4 \cdot {9^m}} \对），$$

对于每个非零整数m被构造。这是第一个不属于具有经典参数的无限类。结果表明，任何平衡的加权矩阵都等价于五类关联方案。