Game of Sloanes: best known packings in complex projective space

John Jasper; Emily J. King; Dustin G. Mixon

doi:10.1117/12.2527956

9 September 2019 Game of Sloanes: best known packings in complex projective space

John Jasper, Emily J. King, Dustin G. Mixon

Proceedings Volume 11138, Wavelets and Sparsity XVIII; 111381E (2019) https://doi.org/10.1117/12.2527956
Event: SPIE Optical Engineering + Applications, 2019, San Diego, California, United States

Abstract

It is often of interest to identify a given number of points in projective space such that the minimum distance between any two points is as large as possible. Such configurations yield representations of data that are optimally robust to noise and erasures. The minimum distance of an optimal configuration not only depends on the number of points and the dimension of the projective space, but also on whether the space is real or complex. For decades, Neil Sloane’s online Table of Grassmannian Packings has been the go-to resource for putatively or provably optimal packings of points in real projective spaces. Using a variety of numerical algorithms, we have created a similar table for complex projective spaces. This paper surveys the relevant literature, explains some of the methods used to generate the table, presents some new putatively optimal packings, and invites the reader to competitively contribute improvements to this table.

Citation Download Citation

John Jasper, Emily J. King, and Dustin G. Mixon "Game of Sloanes: best known packings in complex projective space", Proc. SPIE 11138, Wavelets and Sparsity XVIII, 111381E (9 September 2019); https://doi.org/10.1117/12.2527956

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available