Enumeration of MOLS of small order

DOI10.1090/mcom/3010zbMath1332.05025arXiv1406.3681OpenAlexW1863540423MaRDI QIDQ2792342

Ian M. Wanless, Judith Egan

Publication date: 9 March 2016

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.3681

zbMATH Keywords

Latin squaretransversalMOLSplexorthogonal mate

Mathematics Subject Classification ID

Design of statistical experiments (62K99) Orthogonal arrays, Latin squares, Room squares (05B15) Transversal (matching) theory (05D15)

Related Items (21)

On the non-existence of extended 1-perfect codes and MDS codes ⋮ Construction of generalized minimum aberration three-level orthogonal arrays with three, four and five columns ⋮ Uniform semi-Latin squares and their pairwise-variance aberrations ⋮ Orthogonal trades and the intersection problem for orthogonal arrays ⋮ Further results on the classification of MDS codes ⋮ Unnamed Item ⋮ Diagonal groups and arcs over groups ⋮ Finding the dimension of a non-empty orthogonal array polytope ⋮ Autoparatopisms of Quasigroups and Latin Squares ⋮ Finding the symmetry group of an LP with equality constraints and its application to classifying orthogonal arrays ⋮ Parity of sets of mutually orthogonal Latin squares ⋮ Local permutation polynomials and the action of e-Klenian groups ⋮ Enumeration of sets of mutually orthogonal Latin rectangles ⋮ Pairs of MOLS of order ten satisfying non-trivial relations ⋮ The number of labeled \(n\)-ary abelian groups and totally symmetric medial quasigroups ⋮ On the construction of triples of diagonal Latin squares of order 10 ⋮ Tic-Tac-Toe on an Affine Plane of order 4 ⋮ The number of different reduced complete sets of MOLS corresponding to \(\mathrm{PG} (2,q)\) ⋮ Enumerating extensions of mutually orthogonal Latin squares ⋮ On propositional coding techniques for the distinguishability of objects in finite sets ⋮ Integer Programming for Classifying Orthogonal Arrays

Uses Software

• nauty
• Traces
• libexact

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Indivisible partitions of Latin squares
• Classification algorithms for codes and designs
• Latin squares without orthogonal mates
• The existence of Latin squares without orthogonal mates
• The number of transversals in a Latin square
• Maximal difference matrices of order \(\leq 10\)
• Complete sets of pairwise orthogonal Latin squares and the corresponding projective planes
• Maximal sets of Latin squares and partial transversals
• Perfect factorisations of bipartite graphs and Latin squares without proper subrectangles
• Aspects of complete sets of \(9\times 9\) pairwise orthogonal latin squares
• The number of different reduced complete sets of MOLS corresponding to \(\mathrm{PG} (2,q)\)
• The non-existence of maximal sets of four mutually orthogonal Latin squares of order 8
• On the number of transversal designs
• Monogamous latin squares
• Practical graph isomorphism. II.
• On the number of Latin squares
• Latin Squares with Restricted Transversals
• The number of Latin squares of order 11
• Small latin squares, quasigroups, and loops
• Atomic Latin squares of order eleven
• The structure of conjugacy closed loops
• The existence and construction of two families of designs for two successive experiments
• THE 7 × 7 SQUARES
• A generalization of transversals for Latin squares

This page was built for publication: Enumeration of MOLS of small order