Quasi - Latin designs and their use in glasshouse exper - 1 iments

This paper gives a general method for constructing quasi-Latin square, quasi-Latin 12 rectangle and extended quasi-Latin rectangle designs for symmetric factorial experiments. Two 13 further methods are given for parameter values satisfying certain conditions. Designs are 14 constructed for a range of numbers of rows and columns so that the different construction 15 techniques are illustrated. For some row and column combinations, different designs are com16 pared, including designs constructed using computer search algorithms. The construction of 17 designs with rows and columns that are nested or contiguous is also discussed. 18