I’ve spent half a year on a project to Kubernetes project. During that time we did production deployments of .net core web services to docker.
My main suggestion would be to follow the example on docker.com.
Do you want to send a comment or give me a hint about any issues with a blog post: Open up an issue on GitHub.
Do you want to fix an error or add a comment published on the blog? You can do a fork of this post and do a pull request on github.