This evening next idea visited me: why not to write program for the automatical generation of names of large numbers.
Then I wrote in Pascal the program, which generates names of numbers, according this system, and also this program writes expressions in Latex for each number.
As you can see it is very simply: three nested 20-step-cycles are working for expression .
Below are about 8000 names of numbers with expressions in Latex. They were not written by human, but by this program during just several seconds.
This way, using rules of mentioned system of names as well as using more complex FGH-expressions and more than three nested cycles it is very simply to generate and to write any amount of names of large numbers
Note 1. only one difference with this definition: the code of 'multiplication' has been written as 'ult' (also I would write code of 'tetration' as 'etr')
Note 2. for a 'vig' also can be written as 'bizer' (bi+zero)
result of program working (about 8 000 names and expressions) you can see below (just click links):