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What are the latest and best results on the asymptotic upper bound for the minimum angle between any pair of rays among $n$ rays in $\mathbb{R}^3$?

Any helpful answer would be appreciated. Thank you!

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    $\begingroup$ There is a large science devoted to this very question. Look for "spherical codes" $\endgroup$
    – Fedor Petrov
    Commented Sep 23 at 15:08
  • $\begingroup$ @FedorPetrov Thank you for your comment. However, do the tables on spherical codes contain asymptotic upper bound results? Thanks. $\endgroup$
    – Don
    Commented Sep 23 at 23:31
  • $\begingroup$ Certainly. Look for Kabatiansky - Levenshtein and beyond $\endgroup$
    – Fedor Petrov
    Commented Sep 24 at 4:35
  • $\begingroup$ @FedorPetrov Then what is the expression for the bound? Thank you. $\endgroup$
    – Don
    Commented Sep 25 at 8:02
  • $\begingroup$ Ah, I missed that the dimension 3 is fixed. Then you pack disjoint equal small caps on the sphere. The optimal density is the same as for packing disjoint disks on the plane (you know, locally the Earth is flat), i. e., hexagonal $\endgroup$
    – Fedor Petrov
    Commented Sep 25 at 9:00

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