# New bounds for pairwise orthogonal diagonal Latin squares

@article{Du1993NewBF, title={New bounds for pairwise orthogonal diagonal Latin squares}, author={B. Du}, journal={Australas. J Comb.}, year={1993}, volume={7}, pages={87-100} }

A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. Let dr be the least integer such that for all n > dr there exist r pairwise orthogonal diagonal Latin squares of order n. In a previous paper Wallis and Zhu gave several bounds on the dr. In this paper we shall present some constructions of pairwise orthogonal diagonal Latin squares and consequently obtain new bounds for five pairwise orthogonal diagonal Latin squares.

#### 3 Citations

More mutually orthogonal Latin squares

- Mathematics, Computer Science
- Australas. J Comb.
- 1992

In this paper, some constructions of pairwise orthogonal diagonal Latin squares are given which are useful in the study of Pairwise Orthogonal diagonal Latin squares. Expand

On the existence of self-orthogonal diagonal Latin squares

- Mathematics, Computer Science
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This paper shall present some constructions of self-orthogonal diagonal Latin squares of order 10, and consequently consider the existence ofSelf-ortho-diagonal Latin squares, and present some examples of these constructions. Expand

Some constructions for t pairwise orthogonal diagonal Latin squares based on difference matrices

- Computer Science, Mathematics
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Differing matrices, quasi-difference matrices and holey quasi- Difference Matrices are used to construct t pairwise orthogonal diagonal Latin squares of order v in this paper. Expand

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