Exporting a Blu-Ray compatible MKV with AC3 audio from Premiere Pro?

Title says it all. It doesn’t need the mkv container, I can remux into an mkv, but really what I need is to be able to export the video and audio in the correct format and size

For video, there are 264 blu-ray presets in the dropdown list that will generally work fine. The defaults should include black bars (1920x1080, 1280x720, etc) and you should just be able to just set your bitrate and other quality settings and go. Note that if you select 264 (non-bluray) option, your default dimensions are your project dimensions, rather than full screen HD. The 264 bd preset saves unmuxed files that you can put into an mkv.

I forget if premiere does AC3. If it does not, you could export lossless audio and re-encode it from audacity.