## 28 Citations

### Nonexistence of tight spherical design of harmonic index 4

- Mathematics
- 2014

We give a new upper bound of the cardinality of a set of equiangular lines in $\R^n$ with a fixed angle $\theta$ for each $(n,\theta)$ satisfying certain conditions. Our techniques are based on…

### A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4

- MathematicsEur. J. Comb.
- 2016

### Half of an antipodal spherical design

- Mathematics
- 2017

We investigate several antipodal spherical designs on which we can choose half of the points, one from each antipodal pair, such that they are balanced at the origin. In particular, root systems of…

### Linear Programming Bounds for Spherical (k,k)-Designs

- Mathematics
- 2020

We derive general linear programming bounds for spherical $(k,k)$-designs. This includes lower bounds for the minimum cardinality and lower and upper bounds for minimum and maximum energy,…

### Spherical two-distance sets and related topics in harmonic analysis

- Mathematics
- 2014

The semidefinite programming method is used to find the maximum size for equiangular line sets in R and a method of constructing spherical two-distance sets that also form tight frames that also forms a tight frame for R is suggested.

### More on spherical designs of harmonic index $t$

- Mathematics
- 2015

A finite subset $Y$ on the unit sphere $S^{n-1} \subseteq \mathbb{R}^n$ is called a spherical design of harmonic index $t$, if the following condition is satisfied: $\sum_{\mathbf{x}\in…

### On Spherical Designs of Some Harmonic Indices

- MathematicsElectron. J. Comb.
- 2017

The classification (non-existence) of tight spherical designs of harmonic index 6 and 8, as well as the asymptotic non-existence of Tight spherical designsof harmonic index $2e$ for general $e\geq 3$ are shown.

### Upper bounds for energies of spherical codes of given cardinality and separation

- Computer ScienceDes. Codes Cryptogr.
- 2020

A linear programming framework for obtaining upper bounds for the potential energy of spherical codes of fixed cardinality and minimum distance is introduced using Hermite interpolation and polynomials are constructed.

### Upper bounds for energies of spherical codes of given cardinality and separation

- Computer ScienceDesigns, Codes and Cryptography
- 2020

A linear programming framework for obtaining upper bounds for the potential energy of spherical codes of fixed cardinality and minimum distance is introduced using Hermite interpolation and polynomials are constructed.

## References

SHOWING 1-10 OF 17 REFERENCES

### Optimal asymptotic bounds for spherical designs

- Mathematics
- 2010

In this paper we prove the conjecture of Korevaar and Meyers: for each $N\ge c_dt^d$ there exists a spherical $t$-design in the sphere $S^d$ consisting of $N$ points, where $c_d$ is a constant…

### A survey on spherical designs and algebraic combinatorics on spheres

- MathematicsEur. J. Comb.
- 2009

### Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators

- Mathematics
- 2005

Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group…

### Infinite groups : geometric, combinatorial and dynamical aspects

- Mathematics
- 2005

Parafree Groups.- The Finitary Andrews-Curtis Conjecture.- Cuts in Kahler Groups.- Algebraic Mapping-Class Groups of Orientable Surfaces with Boundaries.- Solved and Unsolved Problems Around One…

### Well-Separated Spherical Designs

- Mathematics
- 2013

For each $$N\ge C_dt^d$$N≥Cdtd, we prove the existence of a well-separated spherical $$t$$t-design in the sphere $$S^d$$Sd consisting of $$N$$N points, where $$C_d$$Cd is a constant depending only on…