Weak and Strong Nestings of BIBDs
Douglas R. Stinson

TL;DR
This paper investigates two nesting types of BIBDs, establishing lower bounds on the number of added points and identifying classes with optimal nestings, advancing combinatorial design theory.
Contribution
It introduces and analyzes weak and strong nestings of BIBDs, providing lower bounds and constructing optimal examples for specific parameters.
Findings
Lower bounds on the number of new points in nestings.
Infinite classes of BIBDs with optimal nestings identified.
Characterization of weak and strong nesting properties.
Abstract
We study two types of nestings of balanced incomplete block designs (BIBDs). In both types of nesting, we wish to add a point (the nested point) to every block of a -BIBD in such a way that we end up with a partial -BIBD for some . In the case where , we are introducing new points. This is called a weak nesting. A strong nesting satisfies the stronger property that no pair containing a new point occurs more than once in the partial -BIBD. In both cases, the goal is to minimize . We prove lower bounds on as a function of , and and we find infinite classes of - and -BIBDs that have optimal nestings.
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Taxonomy
TopicsAdvanced Data Storage Technologies
