In this paper, we provide a criterion for determining whether multiple shells support a $t$-design. We construct as a corollary an infinite series of $2$-designs using power residue codes.

翻译：本文给出了一个判定多个球壳是否支撑$t$-设计的准则。作为推论，我们利用幂剩余码构造了一个无穷$2$-设计序列。