Orbits of infinite block designs

Resolvability of Infinite Designs

In this paper we examine the resolvability of infinite designs. We show that in stark contrast to the finite case, resolvability for infinite designs is fairly commonplace. We prove that every t-(v, k,Λ) design with t finite, v infinite and k, λ < v is resolvable and, in fact, has α orthogonal resolutions for each α < v. We also show that, while a t-(v, k,Λ) design with t and λ finite, v infini...

Block Intersection Numbers of Block Designs Ii

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, ...

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...

Nested Block Designs

1. Introduction Heterogeneity in the experimental material is the most important problem to be reckoned within the statistical design of scientific experiments. As if it is not suitably taken care of, in designing of an experiment, is likely to over shadow the real treatment differences making them remain undetected, unless they are large enough. Occasionally, one can find a certain factor (cal...