Hamming空间中差异的界
Bounds for discrepancies in the Hamming space
摘要：
我们推导出球$L_p$的界限-差异在汉明空间$0<p<\infty$和$p=\infty$。对于许多空间，如欧几里得球面和更一般的紧致黎曼流形，已经得到了精确的误差估计。在本文中，我们表明，在Hamming空间的差异的行为从根本上不同，因为在这个空间中的球的体积取决于它的半径指数，而这种依赖的黎曼流形是多项式。
英文摘要：
We derive bounds for the ball $L_p$-discrepancies in the Hamming space for $0<p<\infty$ and $p=\infty$. 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.
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