The existence of 2x4 grid-block designs and their applications

Abstract

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 x c arrays with elements in V. A pair ( V, A) is called an r x 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 x 3 grid-block designs. Meanwhile, the existence of 2 x 3 grid-block designs was shown by Carter [ Designs on Cubic Multigraphs, Ph. D. thesis, McMaster University, Hamilton, ON, Canada, 1989] by decomposing K-v into cubic graphs. In this paper, we show the existence of 2 x 4 grid-block designs.