Playing with finite sets

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Hello, I would like to know if anyone can give me some hint to do the following to the next level without repeating all routines below for m=5, where m is the number of elements fo M:

p = dict()
M = FiniteEnumeratedSet([1 .. 4])
P = cartesian_product([M]*4)
for i in (1 .. 4):
   for u in (1 .. 4):
      p[i, u] = [1 if P[m][i-1] == u else 0 for m in (0 .. 255)]
P1 = matrix([p[i,j] for i in (1..4) for j in (1..4)])

and

for i in (1 .. 4):
   for u in (1 .. 4):
       for j in (1..4):
          for v in (1..4):
             if i <= j:
                p[i,j, u,v] = [1 if P[m][i-1] == u and P[m][j-1] == v else 0 for m in (0 .. 255)]
P2 = matrix([p[i,j,u,v] for i in (1..4) for j in (1..4) for u in (1..4) for v in (1..4) 
        if i <= j])

and

for i in (1 .. 4):
   for u in (1 .. 4):
      for j in (1..4):
         for k in (1..4):
            for v in (1..4):
               for w in (1..4):
                  if i <= j and j <= k:
                     p[i,j,k, u,v,w] = [1 if P[m][i-1] == u and 
                                               P[m][j-1] == v and 
                                               P[m][k-1] == w else 0 for m in (0 .. 255)]
P3 = matrix([p[i,j,k, u,v,w] for i in (1..4) for j in (1..4) for u in (1..4) for v in (1..4) for k in (1..4) for w in (1..4) if i <= j and j <= k])

and finally

P1.rank()
P2.rank()
P3.rank()