Digital nets (in base 2) are the subsets of [0,1]d that contain exactly the expected number of points in every not-too-small dyadic box. We construct finite sets, which we call "almost nets", such that every such dyadic box contains almost the expected number of points from the set, but whose size is exponentially smaller than the one of nets. We also establish a lower bound on the size of such almost nets.
@article{10_37236_10791,
author = {Boris Bukh and Ting-Wei Chao},
title = {Digital almost nets},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {4},
doi = {10.37236/10791},
zbl = {1520.11072},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10791/}
}
TY - JOUR
AU - Boris Bukh
AU - Ting-Wei Chao
TI - Digital almost nets
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/10791/
DO - 10.37236/10791
ID - 10_37236_10791
ER -
%0 Journal Article
%A Boris Bukh
%A Ting-Wei Chao
%T Digital almost nets
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/10791/
%R 10.37236/10791
%F 10_37236_10791
Boris Bukh; Ting-Wei Chao. Digital almost nets. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/10791
