# Game of Sloanes: Best known packings in complex projective space

## TL;DR

This paper introduces a comprehensive table of optimal point packings in complex projective spaces, using numerical algorithms, and invites community contributions to improve these configurations for applications requiring noise robustness.

## Contribution

It creates the first extensive table of putatively optimal packings in complex projective spaces and discusses methods for generating and improving these configurations.

## Key findings

- New putatively optimal packings identified
- Numerical algorithms effectively generate packings
- Community invited to contribute improvements

## 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.