Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved Lower Bounds for Strongly Separable Matrices and Related
  Combinatorial Structures   In nonadaptive group testing, the main research objective is to design an
efficient algorithm to identify a set of up to $t$ positive elements among $n$
samples with as few tests as possible. Disjunct matrices and separable matrices
are two classical combinatorial structures while one provides a more efficient
decoding algorithm and the other needs fewer tests, i.e., larger rate.
Recently, a notion of strongly separable matrix has been introduced, which has
the same identifying ability as a disjunct matrix, but has larger rate. In this
paper, we use a modified probabilistic method to improve the lower bounds for
the rate of strongly separable matrices. Using this method, we also improve the
lower bounds for some well-known combinatorial structures, including locally
thin set families and cancellative set families.

37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th