15  29  1  43 
31  27  19  11 
25  9  33  21 
17  23  35  13 




01 
02 
03 
04 
05 
06 
07 
08 

09 
10 
11 
12 
13 
14 
15 
16 

17 
18 
19 
20 
21 
22 
23 
24 

25 
26 
27 
28 
29 
30 
31 
32 
The first and the second CF are strong equivalent (via transformation 02), and the first and third CF are
equivalent (via transformation 14). In strings: (1122 3456 5768 4873) is strong equivalent to (1234 1526 7863 7458), (1122 3456 5768 4873) is equivalent to (1212 3456 5768 8347). 
EC01: (1122 3344 5566 7788), equivalent CF: 4 [Dudeney IV,V] 
EC02: (1122 3443 5665 7788), equivalent CF: 8 [Dudeney IX,VIII,VII,X] 
EC03: (1122 3456 7788 4365), equivalent CF: 8 [Dudeney XI,XII] 
EC04: (1122 3456 5678 8347), equivalent CF: 32 
EC05: (1122 3456 5768 4873), equivalent CF: 32  EC06: (1122 3443 7878 6543), equivalent CF: 16 
EC07: (1122 3456 6783 8547), equivalent CF: 16 
EC08: (1221 3443 5665 7887), equivalent CF: 2 [Dudeney VI] 
EC09: (1234 5167 7385 2648), equivalent CF: 16 
EC10: (1234 5678 8765 4321), equivalent CF: 1 [Dudeney III] 
EC11: (1234 2567 8653 4871), equivalent CF: 8 
EC12: (1234 2143 5678 6587), equivalent CF: 2 [Dudeney II,I] 
(S01) The set T_{17}={1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17} allows 260 reduced GMS, therefore 32*260=8320 GMS (compare with classical magic squares).
That this number cannot be surpassed, is an old conjecture (see references below) and til today scientifically unproved, as well as the question whether there are other vectors than the named 154 ones . There are symmetric sets, which allow as many GMS, as there are classical 4x4 magic squares, namely 7040. But the structure of these GMS can be rather different from the structure of classical magic squares (see Vectors154.pdf). 

1  16  4  13 
6  11  7  10 
15  2  14  3 
12  5  9  8 