Balanced incomplete block design
A block design on a set of points and blocks (sets of points) which is "balanced": each block is of the same size, each point appears in the same number of blocks and each pair of points occurs in the same number of blocks; and "incomplete", not in general the complete collection of sets of given size. Equivalently, a $2$-design.
See Block design for further details and references.
BIBD. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=BIBD&oldid=43163