[GAP Forum] Range of List Iteration

[Sandeep Murthy]

Hello.

I am currently working on GAP programs which search for triples of distinct proper subsets 
of finite groups satisfying a certain property.  For a group G of order n, the space of 
triples of distinct proper subsets is of order 8^n.  By applying a certain filter to filter out ineligible
triples, I am searching actually on a much smaller space of order 4^n, but still exponential
in the group order n.

I'm currently using "binary list" representations of group subsets, where a given subset
X of G is represented by a unique n-length list b(X) of 0's and 1's and a corresponding unique 
decimal number d(X) in the range [1..2^n].  The program iterates over all distinct proper subset 
triples of G by running through all possible triples of n-bit combinations of 1's and 0's, and 
testing the property for the equivalent subset triple.

The programs work fine for groups of order n <= 27, but not for n >= 28 - GAP says that a
loop cannot over a range >= 2^28. Is this an absolute limit, or is this machine dependent?

Sincerely, Sandeep.