A
design or
BIBD (
Balanced Incomplete Block Design) with
parameters (
v, k, lambda, r, b) is an
incidence system (the name '
Design' comes from the original use of these
combinatorial structures in the design of
industrial and
agricultural experiments) in which a set of v 'points' is partitioned into b 'blocks' in such a way that any two
points determine
lamda blocks. There are k
points in every
block, and each
point is contained in r different
blocks. In a more general form, a
t-Design (with
t > 2) has the property that any
t points determine
lambda blocks.
The
prototypical example of a
design is the
projective space of
dimension 2 over
GF(2) aka the
Fano plane, which is a design with
parameters (
v=7,
k=3,
lambda=1,
r=3 and
b=7) this is also an example of a
symmetric design and a
Steiner triple system.
--back to
combinatorics--