# Block Design

In combinatorial mathematics, a block design is a set together with a family of subsets (repeated subsets are allowed at times) whose members are chosen to satisfy some set of properties that are deemed useful for a particular application. These applications come from many areas, including experimental design, finite geometry, software testing, cryptography, and algebraic geometry. Many variations have been examined, but the most intensely studied are the balanced incomplete block designs (BIBDs or 2-designs) which historically were related to statistical issues in the design of experiments.

A block design in which all the blocks have the same size is called uniform. The designs discussed in this article are all uniform. Pairwise balanced designs (PBDs) are examples of block designs that are not necessarily uniform.

### Other articles related to "block design, blocks, block, design, block designs, designs":

Durbin Test - Background
... See also Blocking (statistics) In a randomized block design, k treatments are applied to b blocks ... In a complete block design, every treatment is run for every block and the data are arranged as follows Treatment 1 Treatment 2 Treatment k Block 1 X11 X12 X1k Block 2 X21 X22 X2k ... In this case, it is strongly recommended to run a balanced incomplete design ...
Block Design - Applications
... The mathematical subject of block designs originated in the statistical framework of design of experiments ... These designs were especially useful in applications of the technique of analysis of variance (ANOVA) ... This remains a significant area for the use of block designs ...
Fundamental Combinatorial Designs
... The classical core of the subject of combinatorial designs is built around balanced incomplete block designs (BIBDs), Hadamard matrices and Hadamard designs, symmetric BIBDs, Latin ... Other combinatorial designs are related to or have been developed from the study of these fundamental ones ... A balanced incomplete block design or BIBD (usually called for short a block design) is a collection B of b subsets (called blocks) of a finite set X of v elements ...

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