Given k points in \(S^1\) satisfying certain conditions which are determined through their symmetric functions, we introduce a method for constructing spherical t-designs in \(\mathbb {R}^2\) with \(2t+k\) elements. This approach points toward a better understanding of the space of spherical t-designs as well as provides a systematic way to obtain examples.

中文翻译：

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$$\pmb {\mathbb {R}^2}$$ R 2 中的对称函数和球面 t 设计

鉴于ķ个\（S ^ 1 \）满足它们通过它们的对称函数确定的某些情况下，我们引入用于构造球形的方法吨-designs在\（\ mathbb {R} ^ 2 \）与\（2T + K \)元素。这种方法有助于更好地理解球形t设计的空间，并提供了一种获取示例的系统方法。