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.