On the Dispersion of Sparse Grids
arXiv:1709.0298323 citations
Originality Incremental advance
AI Analysis
Provides a simple construction with provably near-optimal dispersion for high-dimensional problems, relevant to numerical integration and discrepancy theory.
The authors construct point sets in the d-dimensional unit cube that intersect every axis-aligned box of volume > ε, achieving near-optimal dispersion for a wide range of ε and d.
For any natural number $d$ and positive number $\varepsilon$, we present a point set in the $d$-dimensional unit cube $[0,1]^d$ that intersects every axis-aligned box of volume greater than $\varepsilon$. These point sets are very easy to handle and in a vast range for $\varepsilon$ and $d$, we do not know any smaller set with this property.