Partial design

Origin
The term was introduced and used in Bose and Nair's 1939 paper, and further developed and Bose and Shimamoto's 1952 paper.

Definition
A partial design is a tactical configuration whose point set is equipped with an association scheme such that the number of blocks incident on two distinct points depends only on the equivalence class of that pair with respect to the association scheme.

The class number of a partial design is the number of partitions in the corresponding association scheme. A partial design with class number 1 is a design.

Partial design is also called partial BIBD or partially balanced incomplete block design.