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Academic Journal of Mathematical Sciences, 2025, 6(2); doi: 10.25236/AJMS.2025.060213.

Row-Column Block Designs with Blocks of Size Three

Author(s)

Xiao Nie

Corresponding Author:
Xiao Nie
Affiliation(s)

School of Computing and Mathematical Sciences, University of Waikato, Private Bag, 3105, Hamilton, 3240, New Zealand

Abstract

In this study, we construct row-column designs with three elements per cell and with the following properties: (1) the blocks formed by the cells form a balanced incomplete block design; (2) the rows are regular, in the sense that each element occurs the same number of times in each row; and (3) the columns are near-regular, meaning there is an integer x such that each element occurs either x or x + 1 times. This generalizes the work done in (Seema, Cini and Eldho, 2016) in which such row-column designs are constructed with block size 2. The constructions make use of known solutions to Heffter’s Difference Problem.

Keywords

Row-Column Designs, Heffter Difference Sets, Balanced Incomplete Block Design (BIBD)

Cite This Paper

Xiao Nie. Row-Column Block Designs with Blocks of Size Three. Academic Journal of Mathematical Sciences (2025), Vol. 6, Issue 2: 90-101. https://doi.org/10.25236/AJMS.2025.060213.

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