## Generating an equidistributed net on a sphere using random rotations.(English)Zbl 07457128

Summary: We develop a randomized algorithm (that succeeds with high probability) for generating an $$\varepsilon$$-net in a sphere of dimension $$n$$. The basic scheme is to pick an alphabet consisting of $$O (n\ln (1/\varepsilon )+\ln (1/\delta ))$$ random rotations, form all possible words of length $$O (n\ln (1/\varepsilon ))$$ from this alphabet, and require these words act on a fixed point. We show the set of points so generated is equidistributed at a scale of $$\varepsilon$$.

### MSC:

 68W20 Randomized algorithms 52C10 Erdős problems and related topics of discrete geometry
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### References:

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