On tight spherical designs

By Gabriele Nebe, B. Venkov. 2012

98 citations recorded by the source corpus.

Let X be a tight t-design of dimension n for one of the open cases t=5 or t=7. An investigation of the lattice generated by X using arithmetic theory of quadratic forms allows to exclude infinitely many values for n.

Subfields: Algebra and Number Theory, Materials Chemistry, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f0af295337b98e4336876804933406a286b23095

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Alexey A. Glazyrin
2. Gerhard Zauner
3. Wei-Hsuan Yu

In Materials Chemistry

1. Alexey A. Glazyrin
2. Gerhard Zauner
3. Wei-Hsuan Yu

In Numerical Analysis

1. Alexey A. Glazyrin
2. Gerhard Zauner
3. Wei-Hsuan Yu

Citations in the corpus

• QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY (2011, background): “8] for affine designs) and the non-existence proofs for tight t-designs with r = 1 (see [6], [7], [10]).”
• Upper bounds for $s$-distance sets and equiangular lines (2016, background): “This follows from the non-existence of tight spherical 2s-designes for s ≥ 3 [9].”