Balanced semi-Latin rectangles: properties, existence and constructions for block size two

Nseobong Peter Uto*, R. A. Bailey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
1 Downloads (Pure)

Abstract

There exists a set of designs which form a subclass of semi-Latin rectangles. These designs, besides being semi-Latin rectangles, exhibit an additional property of balance; where no two distinct pairs of symbols (treatments) differ in their concurrences, that is, each pair of distinct treatments concur a constant number of times in the design. Such a design exists for a limited set of parameter combinations. We designate it a balanced semi-Latin rectangle (BSLR) and give some properties, and necessary conditions for its existence. Furthermore, algorithms for constructing the design for experimental situations where there are two treatments in each row-column intersection (block) are also given.
Original languageEnglish
Article number51
Number of pages11
JournalJournal of Statistical Theory and Practice
Volume14
Issue number3
Early online date8 Jul 2020
DOIs
Publication statusPublished - Sept 2020

Keywords

  • Balanced incomplete block design (BIBD)
  • Balanced semi-Latin rectangle (BSLR)
  • Optimal design
  • Quotient block design (QBD)
  • Regular-graph design (RGD)

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