On μ-resolvable BIB designs

Thickly-resolvable block designs

We show that the necessary divisibility conditions for the existence of a σ-resolvable BIBD(v, k, λ) are sufficient for large v. The key idea is to form an auxiliary graph based on an [r, k]-configuration with r = σ, and then edge-decompose the complete λ-fold graph K (λ) v into this graph. As a consequence, we initiate a similar existence theory for incomplete designs with index λ. ∗ Supported...

Some Block Designs Constructed from Resolvable Designs

LetD be a resolvable 2−(v, k, λ) design, andD′ be a 2−(v′, k′, λ′) design, such that v′ = v k . Further, let r and r′ be replication numbers of a point in D and D′, respectively. Shrikhande and Raghavarao proved that then there exists a 2 − (v′′, k′′, λ′′) design D′′, such that v′′ = v, k′′ = kk′ and λ′′ = r′λ + (r − λ)λ′. If D′ is resolvable, then D′′ is also resolvable. Applying this result, ...

Constructions of nested directed BIB designs

A directed BIB design DB(k, A; v) is a BIB design B(k, 2A; v) in which the blocks are transitively ordered k-tuples and each ordered pair of elements occurs in exactly A blocks. A nested directed BIB design NDB(k, A; v) of form IT2<n<k-l(njn, An)in is a DB(k, A; v) where each block contains E2<n<k-l injn mutually disjoint subblocks, injn subblocks of which are partitIoned into in mutually disjo...

Resolvable Designs with Large Blocks

Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information matrix, and consequently in terms of block concurrences. Equalizing block concurrences for given block sizes is often, but not always, the best strategy. Su...

Notes on the structure of support in BIB designs