There are several different definitions of the term "unital" used throughout various branches of mathematics. In geometric combinatorics, a block design of the form (q^3 + 1, q + 1, 1) is said to be a unital. In particular, then, a unital is a collection P consisting of q^3 + 1 points and arranged into subsets S_0, S_1, ...⊆P so that left bracketing bar S_α right bracketing bar = q + 1 for all α and every pair of distinct points x!=y element P is contained in exactly one S_α.

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