Generalised incomplete Trojan designs

Generalised incomplete (m x n)/k Trojan designs for m replicates of nk treatments based on sets of k cyclic generators are discussed. Normal equations for plots-within-columns, plots-within-blocks and blockswithin-columns treatment effects are developed.The nk treatments are divided into k subsets each of size n and the conditional plotswithin-blocks and blocks-within-columns information matrix for each subset is defined. Efficient conditional treatment estimates are discussed and efficient generators for the various strata are discussed. Balanced (m x n)/k incomplete Trojan designs based on Youden generators are constructed and designs based on multiples of a single generator are discussed. Some ideas for constructing efficient general (m x n)/2 designs are outlined and some advantages of generalised incomplete Trojan designs are discussed.