Kummer configuration

[1] There are three different non-isomorphic ways to select 16 different 6-sets from 16 elements satisfying the above properties, that is, forming a biplane.

The most symmetric of the three is the Kummer configuration, also called "the best biplane" on 16 points.

[2] Following the method of Jordan (1869), but see also Assmus and Sardi (1981),[2] arrange the 16 points (say the numbers 1 to 16) in a 4x4 grid.

There are exactly 11520 permutations of the 16 points that give the same blocks back.

[3][4] Additionally, exchanging the block labels with the point labels yields another automorphism of size 2, resulting in 23040 automorphisms.