Nearly column-orthogonal designs based on leave-one-out good lattice point sets

•Nearly column-orthogonal designs are constructed from leave-one-out GLP sets.•The new designs have a fold-over structure.•The new designs have a better stratification property.

Good lattice point sets have desirable space-filling properties, and many designs with large L1-distance can be obtained by the leave-one-out good lattice point method (Zhou and Xu, 2015). However, there are negatively fully correlated columns in such a design. This is undesirable in the modeling of computer experiments. To overcome such a deficiency, we propose a class of designs based on the leave-one-out good lattice point method, whose columns can be divided into two groups, such that any two columns are column-orthogonal when they are from different groups and nearly column-orthogonal when they are in the same group. The new designs can also estimate the linear effects without being correlated with the second-order effects. Moreover, they have good stratification properties and their L1-distances are comparable with the corresponding designs in Zhou and Xu (2015).