Generalisations
A difference family is a set of subsets of a group such that the order of is, the size of is for all, and every nonidentity element of can be expressed as a product of elements of for some (i.e. both come from the same ) in exactly ways.
A difference set is a difference family with . The parameter equation above generalises to . The development of a difference family is a 2-design. Every 2-design with a regular automorphism group is for some difference family
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