Hadamard configurations and sharp cubic-period bounds for stealth in dimensions 10, 11, and 12
Abstract
We construct explicit, nonlattice periodic point configurations in dimensions $10$, $11$ and $12$ with stealth center density 1/24 and unit-density stealth radius 2·24−1/n. These values exceed those of duals of the current record lattice packings, without claiming to exceed all possible lattices. The construction uses the $24$ sign rows of an order-$12$ Hadamard matrix and their antipodes, projected onto n coordinates. For an arbitrary, not necessarily binary, equally weighted motif with marked period 2ℤn, we prove a sharp 2n-point lower bound for a raw stealth radius at least one and classify equality by antipodal Hadamard configurations. We deduce bounded-complexity optimality, sharp optimality among binary motifs in dimensions $10−−12$, and local maximality under simultaneous perturbations of the motif and the marked period shape. A divisibility argument excludes ordinary equally weighted periodic formal duals. Statements are confined to their indicated classes; no global optimality among arbitrary-period configurations is asserted.
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BibTeX
@misc{park2026hadamard,
title = {{Hadamard configurations and sharp cubic-period bounds for stealth in dimensions 10, 11, and 12}},
author = {Josiah Park},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06148},
eprint = {2611.06148},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06148},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Hadamard configurations and sharp cubic-period bounds for stealth in dimensions 10, 11, and 12
AU - Josiah Park
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06148
UR - https://arxiv.org/abs/2611.06148
AB - We construct explicit, nonlattice periodic point configurations in dimensions $10$, $11$ and $12$ with stealth center density 1/24 and unit-density stealth radius 2·24^−1/n. These values exceed those of duals of the current record lattice packings, without claiming to exceed all possible lattices. The construction uses the $24$ sign rows of an order-$12$ Hadamard matrix and their antipodes, projected onto n coordinates. For an arbitrary, not necessarily binary, equally weighted motif with marked period 2ℤ^n, we prove a sharp 2n-point lower bound for a raw stealth radius at least one and classify equality by antipodal Hadamard configurations. We deduce bounded-complexity optimality, sharp optimality among binary motifs in dimensions $10−−12$, and local maximality under simultaneous perturbations of the motif and the marked period shape. A divisibility argument excludes ordinary equally weighted periodic formal duals. Statements are confined to their indicated classes; no global optimality among arbitrary-period configurations is asserted.
ER -