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Resolutions which are orthogonal to at least one other resolution (RORs) and sets of m mutually orthogonal resolutions (m-MORs) of 2-(v, k, λ) designs are considered. A dependence of the number of nonisomorphic RORs and m-MORs of multiple designs on the number of inequivalent sets of v/k − 1 mutually orthogonal latin squares (MOLS) of size m is obtained. ACM Computing Classification System (1998): G.2.1.∗ This work was partially supported by the Bulgarian National Science Fund under Contract No...

Orthogonal systems.

S.A. Vanstone, R.C. Mullin, M. Deza (1978)

Aequationes mathematicae

Orthogonal systems in vector spaces over finite fields.

Iosevich, Alex, Senger, Steven (2008)

The Electronic Journal of Combinatorics [electronic only]

Orthogonal systems of n-ary operations and codes

J. Ušan (1978)

Matematički Vesnik

Overlapping latin subsquares and full products

Joshua M. Browning, Petr Vojtěchovský, Ian M. Wanless (2010)

Commentationes Mathematicae Universitatis Carolinae

We derive necessary and sufficient conditions for there to exist a latin square of order $n$ containing two subsquares of order $a$ and $b$ that intersect in a subsquare of order $c$ . We also solve the case of two disjoint subsquares. We use these results to show that: (a) A latin square of order $n$ cannot have more than $\frac{n}{m} (\binom{n}{h}) / (\binom{m}{h})$ subsquares of order $m$ , where $h = ⌈ (m + 1) / 2 ⌉$ . Indeed, the number of subsquares of order $m$ is bounded by a polynomial of degree at most $\sqrt{2 m} + 2$ in $n$ . (b) For all $n \geq 5$ there exists a loop of order $n$ in which every...

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