| proposed by | Steven Prestwich s.prestwich@cs.ucc.ie |
BIBD generation is described in most standard textbooks on
combinatorics. A BIBD is defined as an arrangement of v distinct
objects into b blocks such that each block contains exactly k
distinct objects, each object occurs in exactly r different blocks,
and every two distinct objects occur together in exactly lambda
blocks. Another way of defining a BIBD is in terms of its
incidence matrix, which is a v by b binary matrix with
exactly r ones per row, k ones per column, and with a scalar product
of lambda between any pair of distinct rows. A BIBD is therefore
specified by its parameters (v,b,r,k,lambda). An example of a
solution for (7,7,3,3,1) is:
0 1 1 0 0 1 0
1 0 1 0 1 0 0
0 0 1 1 0 0 1
1 1 0 0 0 0 1
0 0 0 0 1 1 1
1 0 0 1 0 1 0
0 1 0 1 1 0 0
Lam's problem (prob025) is that of finding a BIBD with
parameters <111,111,11,11,1>.