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I would like to generate elements of finite filed $GF(3^{15})$. To do so I have used the following code :

F.<x> = GF(3^15)
for i in range(3^15):
    print i,"=>", F.fetch_int(i)

But this code failed to generate elements, occurring errors. On there hand the above code works fine for $GF(3^{2})$ given below:

F.<x> = GF(3^2)
for i in range(3^2):
    print i,"=>", F.fetch_int(i)

Produces:

0 => 0
1 => 1
2 => 2
3 => x
4 => x + 1
5 => x + 2
6 => 2*x
7 => 2*x + 1
8 => 2*x + 2.

Where is the problem?

I would like to generate elements of finite filed $GF(3^{15})$. To do so I have used the following code :

F.<x> = GF(3^15)
for i in range(3^15):
    print i,"=>", F.fetch_int(i)

But this code failed to generate elements, occurring errors. On there hand the above code works fine for $GF(3^{2})$ given below:

F.<x> = GF(3^2)
for i in range(3^2):
    print i,"=>", F.fetch_int(i)

Produces:

0 => 0
1 => 1
2 => 2
3 => x
4 => x + 1
5 => x + 2
6 => 2*x
7 => 2*x + 1
8 => 2*x + 2.

Where is the problem?