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Polynomial Time Construction for Spatially Balanced Latin Squares

Author
Le Bras, Ronan; Perrault, Andrew; Gomes, Carla P.
Abstract
In this paper we propose a construction that generates spatially balanced
Latin squares (SBLSs) in polynomial time. These structures are central to
the design of agronomic experiments, as they avoid biases that are otherwise
unintentionally introduced due to spatial auto-correlation. Previous
approaches were able to generate SBLSs of order up to 35 and required
about two weeks of computation. Our algorithm runs in O(n2) and generates
SBLSs of arbitrary order n where 2n + 1 is prime. For example, this
algorithm generates a SBLS of order 999 in a fraction of a second.
Date Issued
2012-04-17Subject
Quasigroup; Latin Square; Spatially Balanced; Combinatorial Design; Agronomic Field Experiments
Type
technical report