The attached workbook [matevijay=generate random 16-character strings.xlsx] is set up to generate 10,000 random strings of 16 characters (not digits) each composed of digits 0-9 and letters A-Z (uppercase only). It is capable of producing any such combination. It uses a named formula called RANC (Random AlphaNumeric Character) that generates one random alphanumeric character. The named formula uses RANDBETWEEN so the list will regenerate every time you open the file or hit F9. To save it, copy Column A and do a Paste Values to another location.

This method does not guarantee that every value will be unique. It is highly unlikely but possible to have duplicates. By definition, if you require that every value is unique then you are not simulating randomness. I implemented another version [matevijay=generate random 16-character strings with dupe check.xlsx] that checks for (but does not prevent) duplicates but for 10,000 entries it takes a while to recalculate.

If you absolutely require uniqueness then I think a macro is required.