The Steiner System S(5, 8, 24)
Particularly remarkable is the Steiner system S(5, 8, 24), also known as the Witt design or Witt geometry. It was first described by Carmichael (1931) and rediscovered by Witt (1938). This system is connected with many of the sporadic simple groups and with the exceptional 24-dimensional lattice known as the Leech lattice.
The automorphism group of S(5, 8, 24) is the Mathieu group M24, and in that context the design is denoted W24 ("W" for "Witt")
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