  Square lattice designs are often used in trials of new varieties of various
agricultural crops. However, there are no square lattice designs for 36
varieties in blocks of size six for four or more replicates. Here we use three
different approaches to construct designs for up to eight replicates. All the
designs perform well in terms of giving a low average variance of variety
contrasts.
  Supplementary materials are available online.

Methodology;Combinatorics