Construction of Spherical Codes Using the Hopf Fibration

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A new approach to construct spherical codes in R4 is presented, based on properties of the Hopf fibration and inspired by a previous construction on layers of flat tori [1][2]. We use the Hopf foliation of the 3-sphere by tori to construct a two-step algorithm: (i) to choose a torus parametrised by height and (ii) to distribute points in each torus by iterated rotation matrices. Our performance matches the previous method and is expected to surpass it in higher dimensions.