论文标题
锤子空间中差异的范围
Bounds for discrepancies in the Hamming space
论文作者
论文摘要
我们以$ 0 <p <\ infty $和$ p = \ infty $的价格得出了球$ l_p $ -discrepancies $ l_p $ -discrepancies。对于许多空间（例如欧几里得球体和更一般的紧凑型riemannian歧管），已经获得了差异的急剧估计。在本文中，我们表明，锤子空间中差异的行为从根本上有所不同，因为该空间中球的体积指数取决于其半径，而这种依赖性对Riemannian歧管则是多项式的。
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.
