Background: my question at :
I am trying to understand, from a layman's point of view, how to make the best one time pad scheme.
From responses to my above referenced question in another post, I understand now why I should use modular math in the scheme, and that the keyspace should be at least as large as the plaintext space.
So, moving beyond those points, I would like to try to understand the best modular base per given plaintext space. For example:
My alphabet's plaintext space is 40 characters, numbered 0 through 39.
So, I am using mod40 math. But I am only using mod40 math because I read elsewhere that my modular base should equal the size of my plaintext space. But I also know that my OTP will still function if my mod base is less than the size of my plaintext space or more than that size. So, in my example, I could use mod30 math or mod50 math just as well as mod40 math.
Therefore, my question is: what is the importance of the mod base in relation to the plaintext space, and, is there an optimal relationship between the two, and, if so, how can I know the optimal ratio of "mod base/plaintext space" in any OTP system?