Name
Abstract | ||
|---|---|---|
Given a finite set $A \subseteq \mathbb{R}^d$, points $a_1,a_2,\dotsc,a_{\ell} \in A$ form an $\ell$-hole in $A$ if they are the vertices of a convex polytope which contains no points of $A$ in its interior. We construct arbitrarily large point sets in general position in $\mathbb{R}^d$ having no holes of size $2^{7d}$ or more. This improves the previously known upper bound of order $d^{d+o(d)}$ due to Valtr. Our construction uses a certain type of equidistributed point sets, originating from numerical analysis, known as $(t,m,s)$-nets or $(t,s)$-sequences. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1017/S0963548321000195 | Comb. Probab. Comput. |
DocType | Volume | Issue |
Journal | 31 | 1 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Boris Bukh | 1 | 0 | 0.34 |
| Ting-Wei Chao | 2 | 0 | 0.68 |
| Ron Holzman | 3 | 287 | 43.78 |