geoconuk/lean-misc-math
For a fixed angular radius theta in (0, pi/2), the least number M(n, theta) of spherical caps of angular radius theta, centred at points of the unit sphere of R^n, whose union is that whole sphere satisfies (1/n) log M(n, theta) -> -log sin theta as n -> infinity. This is the covering half of Wyner (1967): the elementary volume bound gives the lower bound on the covering number and a random-covering argument gives the upper bound. The statement is given in Mathlib's own vocabulary, as an asymptotic for Metric.coveringNumber of Metric.sphere 0 1 in EuclideanSpace R (Fin n) at chordal radius 2…
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