## Abstract

We consider nonadaptive group testing where each item is placed in a constant number of tests. The tests are chosen uniformly at random with replacement, so the testing matrix has (almost) constant column weights. We show that performance is improved compared to Bernoulli designs, where each item is placed in each test independently with a fixed probability. In particular, we show that the rate of the practical COMP detection algorithm is increased by 31% in all sparsity regimes. In dense cases, this beats the best possible algorithm with Bernoulli tests, and in sparse cases is the best proven performance of any practical algorithm. We also give an algorithm-independent upper bound for the constant column weight case; for dense cases this is again a 31% increase over the analogous Bernoulli result.

Original language | English |
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Title of host publication | Proceedings of IEEE International Symposium on Information Theory, 2016 |

Publisher | IEEE |

Pages | 1381-1385 |

Number of pages | 5 |

ISBN (Print) | 9781509018062 |

DOIs | |

Publication status | Published - 10 Aug 2016 |

Event | 2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: 10 Jul 2016 → 15 Jul 2016 |

### Conference

Conference | 2016 IEEE International Symposium on Information Theory, ISIT 2016 |
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Country | Spain |

City | Barcelona |

Period | 10/07/16 → 15/07/16 |