Impossibility of "meet in the middle" attack for DES with three keys?

Question

Cryptography

Hello everyone, let's say there is such a DES: Ek3(Ek2(Ek1(T))) - I had a question (yes, stupid) - why for the same DES, but with two keys, an attack like "meeting in the middle" is possible, but with three - no?
After all, the principle of an attack with two keys - as I understand it - if DES is like this: DES: Ek2(Ek1(T)) - then the principle is like a nesting doll - I go through all the possible options for k2 56 bits long and write it all down in a table - let's call it m1, and one day I will get to k1, which is an element of k2, and start iterating over k1 - also tabulating the results, let's call it m2. And then I just compare the tables m1 and m2 and match the elements - this will be a "meeting in the middle" - right? BUT, why can't I use the same nesting principle to work with DES with three keys? - by simply creating an m3 table and comparing the matches between the three tables?!

Answer 1

In general, triple DES is described as: Ek3(Dk2(Ek1(T))). The problem of implementing a meeting in the middle is just in this central Dk2.
upd: In general, 3DES is better not to use. Look towards DESX, the time increases only by 2 additional XORs, and the cryptographic strength is the same (seemingly).