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After investigating the $3$-dimensional case [35], we continue to address andclose the problems of optimal ball and horoball packings in truncated Coxeterorthoschemes with parallel faces that exist in $n$-dimensional hyperbolic space$\overline{\mathbb{H}}^n$ up to $n=6$. In this paper, we determine the optimalball and horoball packing configurations and their densities for theaforementioned tilings in dimensions $4 \leq n \leq 6$, where the symmetries ofthe packings are derived from the considered Coxeter orthoscheme groups.Moreover, for each optimal horoball packing, we determine the parameter relatedto the corresponding Busemann function, which provides an isometry-invariantdescription of different optimal horoball packing configurations.

Optimal Ball and Horoball Packings Generated by Simply Truncated Coxeter  Orthoschemes with Parallel Faces in Hyperbolic $n$-space for $4 \leq n \leq  6$