Bounds for discrepancies in the Hamming space

07/19/2020

∙

by   Alexander Barg, et al.

∙

0

∙

share

We derive bounds for the ball L_p-discrepancies in the Hamming space for 0<p<∞ and p=∞. Sharp estimates of discrepancies have been obtained for many spaces such as the Euclidean spheres and more general compact Riemannian manifolds. In the present paper, we show that the behavior of discrepancies in the Hamming space differs fundamentally because the volume of the ball in this space depends on its radius exponentially while such a dependence for the Riemannian manifolds is polynomial.