### Abstract

The notion of grid-block designs was introduced by Fu et al.[J. Statist. Plann. Inference, 119(2):225-236, 2004] for the applications to DNA library screenings based on non-Adaptive group testing. This paper is concentrated on resolvable grid-block coverings with a minimal number of parallel classes, which are called optimal. In particular, we characterize optimal 2 x c resolvable coverings, and prove that an optimal resolvable 2x3 covering of order v exists if and only if v = 0 (mod 6).

Original language | English |
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Pages (from-to) | 111-120 |

Number of pages | 10 |

Journal | Utilitas Mathematica |

Volume | 103 |

Publication status | Published - 1 Jun 2017 |

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### Keywords

- Cartesian product
- DNA library screening
- Excess graph
- Grid-block
- Optimal covering
- Resolvable