The unitary group U(n) is a symmetric space and has the point-symmetry for every point \(x\in U(n)\). A great antipodal set on U(n) is a “good” finite subset of U(n) related to the point-symmetries. On the other hand, a great antipodal set on U(n) is an analogue of a pair of antipodal points on spheres. It is known that a finite subset of a sphere is a tight spherical 1-design if and only if it is a pair of antipodal points. In this paper, we investigate a relation between great antipodal sets on U(n) and design theory on U(n). Moreover, we give a relation between a great antipodal set on U(n) and a Hamming cube graph \({\mathcal {Q}}_n\).

ary群U（n）是一个对称空间，并且对每个点\（x \ in U（n）\）具有点对称性。在一个伟大的反足一套ü（ñ）是一个“好”的穷子集ü（ñ相关点对称）。另一方面，在U（n）上设置的极大对映体类似于球体上的一对对映体点。众所周知，当且仅当它是一对对映点时，球的有限子集才是紧密球面1设计。在本文中，我们探讨大映的集之间的关系ü（ñ）和设计理论的ù（n）。此外，我们给出了U（n）上的极大对映集与汉明立方体图\（{\ mathcal {Q}} _ n \）之间的关系。