I think you are referring to the program, Erasmus+ , which is an improved program from Erasmus? If that is true, then I could say it this way: She introduced to us a better program called Erasmus+ or She introduced a better program called Erasmus+ to us or She introduced a better program to us, called Erasmus+ Note: Better is already a comparative word (good, better best) so no need to use "much" better (redundant) Also, note the differences in the spelling for "program" (US vs British spelling, I chose the shorter version, easier to type!)

i believe what you are trying to say is "she introduced us TO the program"