Editing Incidence structure (section)

====Example: Fano plane====
Consider the block design/hypergraph given by:
<math display="block">\begin{align}
P &= \{1,2,3,4,5,6,7\}, \\[2pt]
L &= \left\{ \begin{array}{ll}
  \{1,2,3\}, & \{1,4,5\}, \\
  \{1,6,7\}, & \{2,4,6\}, \\
  \{2,5,7\}, & \{3,4,7\}, \\
  \{3,5,6\} \end{array} \right\}.
\end{align}</math>

This incidence structure is called the [[Fano plane]]. As a block design it is both uniform and regular.

In the labeling given, the lines are precisely the subsets of the points that consist of three points whose labels add up to zero using [[nim addition]]. Alternatively, each number, when written in [[binary number|binary]], can be identified with a non-zero vector of length three over the [[GF(2)|binary field]]. Three vectors that generate a [[linear subspace|subspace]] form a line; in this case, that is equivalent to their vector sum being the zero vector.