To ensure a unique result from each input square, it is necessary to choose an appropriate aspect of the square. AssocPan does this by rotating each input square if necessary so that the quarter with the smallest corner number, (of the 16 corner numbers of the quarters), is at top left.
If some such strategy is not used, more than one input square can transform to the same output square. For example:
In their book:
MOST-PERFECT PANDIAGONAL MAGIC SQUARES
Their construction and enumeration
Ollerenshaw and Brée say that the given transformation of a reversible square is a unique most-perfect square. But, that requires regarding each of the 8 aspects as a different square. For example:
To get the 48 most-perfect squares it is necessary to transform all 8×48 = 384 aspects of the reversible squares and remove the duplicates.
ReversibleMost-perfect avoids this by choosing an aspect of each reversible square that makes a unique most-perfect square.