New bounds on the number of tests for disjunct matrices

Chong Shangguan*, Gennian Ge

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given n items with at most d of which being positive, instead of testing these items individually, the theory of combinatorial group testing aims to identify all positive items using as few tests as possible. This paper is devoted to a fundamental and thirty-year-old problem in the nonadaptive group testing theory. A binary matrix is called d -disjunct if the Boolean sum of arbitrary d columns does not contain another column not in this collection. Let T(d) denote the minimal t , such that there exists a t × n,d -disjunct matrix with n>t. T(d) can also be viewed as the minimal t such that there exists a nonadaptive group testing scheme, which is better than the trivial one that tests each item individually. It was known that T(d)≥ d+22 and was conjectured that T(d)≥ (d+1)2. In this paper, we narrow the gap by proving T(d)/d2≥ (15+ 33)/24 , a quantity in [6/7,7/8].

Original languageEnglish
Article number7580611
Pages (from-to)7518-7521
Number of pages4
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - Dec 2016
Externally publishedYes


  • Nonadaptive group testing
  • disjunct matrix
  • graph matching number


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