Explanation 8x8 magic square
According to Willem Barink and I is the most perfect 8x8 magic square the Franklin panmagic 8x8 square instead of the complete magic square of Kathleen Ollerenshaw. It is not an important issue, because the 8x8 complete magic square is a transformation of the 8x8 Franklin panmagic square (there are as many 8x8 complete as 8x8 Franklin panmagic squares). In the downloads you find the transformation from Franklin panmagic to complete magic square.
See for mor detailed explanation the analysis of the most perfect (8x8) square.
Construction methods of the 8x8 magic square are:
Use the Medjig method to produce a panmagic (and 4x4 compact) 8x8 magic square.
With Ultra magic, symmetric transformation and basic key method (ultra magic) you can construct ultra magic 8x8 squares.
6x6 in 8x8, concentric and bimagic give special 8x8 magic squares.
With the remaining methods you can construct most perfect (Franklin pan)magic squares.