PreprintCC BY 4.0arXiv
Upper bounds for Jung constants of ℓ1d
Abstract
For every integer k≥1, we prove that each nonempty bounded set in real ℓ14k+1 has an ambient enclosing ball of radius at most $(4k-1)/(4k)$ times its diameter. The bound is sharp in dimension five: J(ℓ15)=3/4. If a Hadamard matrix of order 4k exists, then J(ℓ14k−1)=J(ℓ14k)=J(ℓ14k+1)=(4k−1)/(4k). The upper bound for every k≥1 has been formalized in Lean.
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BibTeX
@misc{li2026upper,
title = {{Upper bounds for Jung constants of $\ell_1^d$}},
author = {Xiao Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14055},
eprint = {2610.14055},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14055},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Upper bounds for Jung constants of ℓ_1^d
AU - Xiao Li
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.14055
UR - https://arxiv.org/abs/2610.14055
AB - For every integer k≥1, we prove that each nonempty bounded set in real ℓ_1^4k+1 has an ambient enclosing ball of radius at most $(4k-1)/(4k)$ times its diameter. The bound is sharp in dimension five: J(ℓ_1^5)=3/4. If a Hadamard matrix of order 4k exists, then J(ℓ_1^4k−1)=J(ℓ_1^4k)=J(ℓ_1^4k+1)=(4k−1)/(4k). The upper bound for every k≥1 has been formalized in Lean.
ER -