The existence of 2 × 4 grid-block designs and their applications

Yukiyasu Mutoh*, Toshio Morihara, Masakazu Jimbo, Hung-Lin Fu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Fu, Hwang, Jimbo, Mutoh, and Shiue [J. Statist. Plann. Inference, to appear] introduced the concept of a grid-block design, which is defined as follows: For a v-set V, let A be a collection of r × c arrays with elements in V. A pair (V, A) is called an r × c grid-block design if every two distinct points i and j in V occur exactly once in the same row or in the same column. This design has originated from the use of DNA library screening. They gave some general constructions and proved the existence of 3 × 3 grid-block designs. Meanwhile, the existence of 2 × 3 grid-block designs was shown by Carter [Designs on Cubic Multigraphs, Ph.D. thesis, McMaster University, Hamilton, ON, Canada, 1989] by decomposing Kv into cubic graphs. In this paper, we show the existence of 2 × 4 grid-block designs.

Original languageEnglish
Pages (from-to)173-178
Number of pages6
JournalSIAM Journal on Discrete Mathematics
Issue number2
StatePublished - 1 Feb 2003


  • Graph decomposition
  • Graph design
  • Grid-block

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