A Simple Approach to Constructing Quasi-Sudoku-based Sliced Space-Filling Designs

TL;DR

This paper introduces a simple method for constructing quasi-Sudoku-based space-filling designs that ensure uniformity in projections, useful for computer experiments and cross-validation, with practical implementation and diverse design options.

Contribution

The paper presents a straightforward construction of doubly orthogonal quasi-Sudoku Latin squares and quasi-sliced orthogonal arrays for generating uniform sliced space-filling designs.

Findings

Achieves uniformity in one and two-dimensional projections for full and sliced designs.

Provides practical construction methods with diverse design sizes and factors.

Enables applications in computer experiments and cross-validation.

Abstract

Sliced Sudoku-based space-filling designs and, more generally, quasi-sliced orthogonal array-based space-filling designs are useful experimental designs in several contexts, including computer experiments with categorical in addition to quantitative inputs and cross-validation. Here, we provide a straightforward construction of doubly orthogonal quasi-Sudoku Latin squares which can be used to generate sliced space-filling designs which achieve uniformity in one and two-dimensional projections for both the full design and each slice. A construction of quasi-sliced orthogonal arrays based on these constructed doubly orthogonal quasi-Sudoku Latin squares is also provided and can, in turn, be used to generate sliced space-filling designs which achieve uniformity in one and two-dimensional projections for the full design and and uniformity in two-dimensional projections for each slice. These constructions are very practical to implement and yield a spectrum of design sizes and numbers of factors not currently broadly available.