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This document gives a generalization on the alphabet size of the method that is described in Nicaud's thesis for randomly generating complete DFAs. First, we recall some properties of m-ary trees and we give a bijection between the set of m-ary trees and the set R(m, n) of generalized tuples. We show that this bijection can be built on any total prefix order on Σ*, Then we give the relations that exist between the elements of R(m,n) and complete DFAs built on an alphabet of size greater than 2. We give algorithms that allow us to randomly generate accessible complete DFAs. Finally, we provide experimental results that show that most of the accessible complete DFAs built on an alphabet of size greater than 2 are minimal.