## Abstract Recently, A. B. Evans proved the following Theorem: There is a maximal set of (p − 3)/2 [(resp. (p − 1)/2] mutually orthogonal Latin squares of order __p__ if __p__ is a prime __p__ ≡ 3 mod 4 (resp. __p__ ≡ 1 mod 4). In this article I will give a slightly different proof using more geom
Maximal difference matrices of order ⩽10
✍ Scribed by Dieter Jungnickel; Gerhard Grams
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 261 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
A (maximal) difference matrix with r rows over a group G of order s gives rise to a (maximal) set of r -1 mutually orthogonal Latin squares of order s. The row sizes of maximal difference matrices are determined for all groups G of order ~<10.
📜 SIMILAR VOLUMES
Koukouvinos, C. and J. Seberry, Hadamard matrices of order =8(mod 16) with maximal excess, Discrete Mathematics 92 (1991) 173-176. Kounias and Farmakis, in 'On the excess of Hadamard matrices', Discrete Math. 68 (1988) 59-69, showed that the maximal excess (or sum of the elements) of an Hadamard mat
We show that if there is a skew-Hadamard matrix of order m then there is an Hadamard matrix of order 4m2 -4m whose excess attains the maximum possible bound predicted by S. Kounias and N. Farmakis, On the excess of Hadamard matrices, Discrete Mathematics 68 (1988) 59-69. That is a(4m\* -4m) = 4(m -1