2 research outputs found
Pooling designs with surprisingly high degree of error correction in a finite vector space
Pooling designs are standard experimental tools in many biotechnical
applications. It is well-known that all famous pooling designs are constructed
from mathematical structures by the "containment matrix" method. In particular,
Macula's designs (resp. Ngo and Du's designs) are constructed by the
containment relation of subsets (resp. subspaces) in a finite set (resp. vector
space). Recently, we generalized Macula's designs and obtained a family of
pooling designs with more high degree of error correction by subsets in a
finite set. In this paper, as a generalization of Ngo and Du's designs, we
study the corresponding problems in a finite vector space and obtain a family
of pooling designs with surprisingly high degree of error correction. Our
designs and Ngo and Du's designs have the same number of items and pools,
respectively, but the error-tolerant property is much better than that of Ngo
and Du's designs, which was given by D'yachkov et al. \cite{DF}, when the
dimension of the space is large enough