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Efficient lifts into odd dimensions of Spherical $5$- and $7$-designs with Balanced Halves

  • Konstantin Delchev
  • Boryan Yordanov
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Abstract

We propose constructions of spherical $5$- and $7$-designs in odd dimensions by lifting balanced halves of even-dimensional designs to several layers of suitable latitudes. For every odd dimension, we obtain an explicit spherical $5$-design with at most 60(d2−1) points, attaining the optimal quadratic order in the dimension. Assuming Zauner's conjecture, this bound improves to 7.5(d−1)2. For every odd d ≥ 9, we also construct a spherical $7$-design with 110M points from a complex projective $3$-design with M points in ℂℙ(d−3)/2.

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Cite

BibTeXRIS
BibTeX
@misc{delchev2026efficient,
  title = {{Efficient lifts into odd dimensions of Spherical $5$- and $7$-designs with Balanced Halves}},
  author = {Konstantin Delchev and Boryan Yordanov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12767},
  eprint = {2610.12767},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12767},
}
RIS
TY  - UNPB
TI  - Efficient lifts into odd dimensions of Spherical $5$- and $7$-designs with Balanced Halves
AU  - Konstantin Delchev
AU  - Boryan Yordanov
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12767
UR  - https://arxiv.org/abs/2610.12767
AB  - We propose constructions of spherical $5$- and $7$-designs in odd dimensions by lifting balanced halves of even-dimensional designs to several layers of suitable latitudes. For every odd dimension, we obtain an explicit spherical $5$-design with at most 60(d^2−1) points, attaining the optimal quadratic order in the dimension. Assuming Zauner's conjecture, this bound improves to 7.5(d−1)^2. For every odd d ≥ 9, we also construct a spherical $7$-design with 110M points from a complex projective $3$-design with M points in ℂℙ^(d−3)/2.
ER  -