Abstract This work introduces the n-dimensional congruent lattices using necklaces, a general methodology to generate uniform distributions in multidimensional modular spaces. The formulation presented in this manuscript constitutes the mathematical foundation of the most used satellite constellation designs, including Walker Constellations, and Lattice and Necklace Flower Constellations. These constellation design models are based on Number Theory and allow to obtain distributions that have some interesting properties of uniformity and large number of symmetries. This work includes the complete formulation of the methodology, proofs for existence and uniqueness of the distribution definitions, and several theorems that focus on the counting possibilities of design for the most common cases of study.

中文翻译：

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使用项链的 n 维全等格子

摘要 这项工作介绍了使用项链的 n 维全等格，这是一种在多维模块化空间中生成均匀分布的通用方法。本手稿中提出的公式构成了最常用的卫星星座设计的数学基础，包括沃克星座、格子和项链花星座。这些星座设计模型基于数论，并允许获得具有一些有趣的均匀性和大量对称特性的分布。这项工作包括方法论的完整表述、分布定义的存在性和唯一性的证明，以及一些侧重于最常见研究案例的设计计数可能性的定理。