How can I use METAFONT to make a font with more than 256 symbols? (Ideally these would be typed in LaTeX using a command.) Alternatively, can I define such a large number of symbols, built in METAFONT, for use in TeX, in any other way?

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    you can not, the tfm format only deals with 256 character fonts. But you have not said what your actual use is. If you need 2560 characters you can make 10 fonts. (this is how support for CJK characters in pdftex works) – David Carlisle Jun 18 '18 at 19:33

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