Block design

In <a href="/facts/Combinatorics/k14xUoKT">combinatorial</a> <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a block design is an <a href="/facts/Incidence_structure/PzqNv9Eq">incidence structure</a> consisting of a set together with a <a href="/facts/Family_of_sets/WbYof7lP">family of subsets</a> known as blocks, chosen such that number of occurrences of each element satisfies certain conditions making the collection of blocks exhibit <a href="/facts/Symmetry/hpu7DK8p">symmetry</a> (balance). Block designs have applications in many areas, including <a href="/facts/Experimental_design/VMrNftbr">experimental design</a>, <a href="/facts/Finite_geometry/GL0nnEk8">finite geometry</a>, <a href="/facts/Physical_chemistry/WqwnJjRM">physical chemistry</a>, <a href="/facts/Software_testing/VoXzG9Tb">software testing</a>, <a href="/facts/Cryptography/e94PEVau">cryptography</a>, and <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a>.
Without further specifications the term block design usually refers to a balanced incomplete block design (BIBD), specifically (and also synonymously) a 2-design, which has been the most intensely studied type historically due to its application in the <a href="/facts/Design_of_experiments/VMrNftbr">design of experiments</a>. Its generalization is known as a t-design.

Block design open-in-new

Block design