Photo from academic.microsoft.com
We prove a lower bound of $\Omega (d^{3/2} \cdot (2/\sqrt{3})^d)$ on the kissing number in dimension $d$. This improves the classical lower bound of Chabauty, Shannon, and Wyner by a… Click to show full abstract
We prove a lower bound of $\Omega (d^{3/2} \cdot (2/\sqrt{3})^d)$ on the kissing number in dimension $d$. This improves the classical lower bound of Chabauty, Shannon, and Wyner by a linear factor in the dimension. We obtain a similar linear factor improvement to the best known lower bound on the maximal size of a spherical code of acute angle $\theta$ in high dimensions.
Keywords:
codes high;
spherical codes;
high dimensions;
numbers spherical;
kissing numbers;
lower bound
Journal Title: Advances in Mathematics
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Advances in Mathematics
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!