Lower Bounds for Cover-Free Families
Ali Z. Abdi, Nader H. Bshouty

TL;DR
This paper establishes new asymptotic lower bounds on the size of cover-free families, which are combinatorial structures with applications in areas like group testing and coding theory, especially when parameters are within certain bounds.
Contribution
It provides novel asymptotic lower bounds for the minimum size of cover-free families under specific parameter constraints, advancing theoretical understanding.
Findings
Derived new asymptotic lower bounds for (w,r)-cover-free families
Applicable when w ≤ r = |F|^ε for ε ≥ 1/2
Enhances understanding of combinatorial limits in cover-free structures
Abstract
Let be a set of blocks of a -set . is called -cover-free family (CFF) provided that, the intersection of any blocks in is not contained in the union of any other blocks in . We give new asymptotic lower bounds for the number of minimum points in a -CFF when for some constant .
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Taxonomy
TopicsLimits and Structures in Graph Theory · Cellular Automata and Applications · Coding theory and cryptography
