Richard Lander, Program Manager on the .NET Team, has published a .NET Core on Docker roadmap.  Here are a few key points taken from his post:

• We are now hardening the runtime to make it container-aware and function efficiently in low-memory environments.
• With .NET Core 3.0, we found ways to significantly improve the performance and reduce the memory used by a large margin.
• We now run the TechEmpower plaintext benchmark in a container limited to about 150 MB, while servicing millions of requests per second.
• PowerShell Core has been added to the .NET Core SDK Docker container images, per requests from the community.
• Microsoft teams are now publishing container images to the Microsoft Container Registry (MCR). 
• For .NET Core 3.0, we intend to publish Debian 10 based images.
• Today, we support Ubuntu 18.04 for all supported .NET Core versions. When 20.04 is released, we will start publishing images based on it, for the latest .NET Core version at that time.
• We are in the process of adding support for ARM64 on Linux with .NET Core 3.0, complementing the ARM32 and X64 support already in place.

And finally this:

• Containers are a major focus for .NET Core