Explanation 16x16 magic square
The 16x16 magic square is not only an even multiple of 4, but it exists of 4x4 magic 4x4 sub-squares, which gives many possibilities to construct a 16x16 magic square. In my opinion you can use the 16x16 magic square to construct the perfect magic square and so it happened!
The methodes to construct 16x16 magic squares are:
Medjig, composite Matroesjka, 14x14 in 16x16, concentric and bimagic are specials.
Use symmetric transformation and basic key method (ultra magic) to construct ultra magic 16x16 squares, which are panmagic, symmetric, 2x2 compact and each 1/4 row/column/diagonal gives 1/4 of the magic sum.
With the remaining methods you get most perfect (= Franklin pan)magic 16x16 squares.
Admire the perfect magic square.