There's a website, I can't remember the link, but any text you search can be found to have already been written on one of its pages.
It used an algorithm to generate every possible page of text in the English language, including gobbledygook and random keyboard smashing.
You can then share a link to a full page of text that is far smaller than the page itself, given infinite computational resources, it would be possible to parse any program or any bit of software into its text equivalent and then generate the URL that attaches to this algorithm for that entire page reducing a thousand characters to 16.
It would then be possible to make a page consisting of these 16 digit characters and then compress that page to another page, turning 70,000 words of text or so into 16 digits.
Once you had a page full of those, you could compress them again by finding a page that contains a link to the links of all of the pages.
Given that this is perfect compression you could literally reduce any file to the URL of the page that you need to use (and some information about how many pages deep you have to go and any needed information on the final file structure and format at the end of the reconstruction) to regenerate the page that you need to use to regenerate the page that you need to use to regenerate the page and so on until you have fully reconstructed the file.
And, given that these pages that can be summoned by a URL and do not actually exist until they are generated by the algorithm, it is entirely feasible that the algorithm itself could be stored on your local computer, meaning that with a somewhat complicated but still reasonable system, you could send a file of any size to any person in a text.
The problem is the computational resources needed to utilize this algorithm. It would have to crunch out the numbers to rebuild every single file that is sent its way and even on a fairly fast system that's going to take some time.
However, if anyone wants to take this idea and run with it I'm pretty sure the world would appreciate your efforts. Since we have the ability to create a page of text using an algorithm then we probably should use that and then once it becomes commonplace I'm sure people will build chiplet accelerators for the process.