The results of computer searches for BIBDs, mostly with cyclic or 1-rotational automorphism groups, with some designs based on other groups (both abelian and non-abelian), are presented as difference families, one initial block per line. The invariant treatment, if present, is denoted by 1000. For each design is given a heading ("Design ... ") with the number in the list, the group size, and the invariants of the graph as calculated by the program. The later searches also include block intersection invariants and, where the group is greater than the cyclic group, generators of the group. (Note that if the group size is very large, it may be printed as 0.) Designs for v = 8,12,15,16,18,20,21,22,24 are, or will be, given via the local menu, with k from 3 to 12 (where applicable) and a restricted range for λ (usually (k-1)). Resolved and Near-Resolved designs are included.
The graph for an unresolved BIBD is constructed with a node for each block and treatment, undirected links between incident blocks and treatments; the treartment nodes are assigned one colour, the blocks another (to use nauty terminology).
(Near-)Resolved designs are assigned nodes of a third colour, the (near-)replicates, with undirected links between them and incident blocks and treatments.
Last Updated on 12/10/2004
By D.H.Rees