Mutually orthogonal Latin squares: A brief survey of constructions

DOI10.1016/S0378-3758(00)00276-7zbMath0991.05020OpenAlexW2044022598MaRDI QIDQ5935426

Jeffrey H. Dinitz, Charles J. Colbourn

Publication date: 2 January 2002

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0378-3758(00)00276-7

zbMATH Keywords

MOLSmutually orthogonal Latin squarespairwise balanced designstransversal designs

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Orthogonal arrays, Latin squares, Room squares (05B15) Steiner systems in finite geometry (51E10) Combinatorial aspects of finite geometries (05B25) Blocking sets, ovals, (k)-arcs (51E21) General block designs in finite geometry (51E05)

Related Items (22)

Clique number of Xor products of Kneser graphs ⋮ Covering arrays, augmentation, and quilting arrays ⋮ The optimal bound on the 3-independence number obtainable from a polynomial-type method ⋮ Parity of sets of mutually orthogonal Latin squares ⋮ Completing the spectrum of \(r\)-orthogonal Latin squares ⋮ Constructing heterogeneous hash families by puncturing linear transversal designs ⋮ A short disproof of Euler's conjecture based on quasi-difference matrices and difference matrices ⋮ Completely reducible super-simple designs with block size four and related super-simple packings ⋮ Construction of group divisible designs and rectangular designs from resolvable and almost resolvable balanced incomplete block designs ⋮ Mutually orthogonal graph squares ⋮ Two spectral characterizations of regular, bipartite graphs with five eigenvalues ⋮ Ovals and hyperovals in nets ⋮ Searching for mutually orthogonal Latin squares via integer and constraint programming ⋮ Linear hash families and forbidden configurations ⋮ Unnamed Item ⋮ Resolvable covering arrays ⋮ Interaction detection in Latin and Hyper-latin squares ⋮ MUTUALLY ORTHOGONAL FAMILIES OF LINEAR SUDOKU SOLUTIONS ⋮ Transversal designs in classical planes and spaces ⋮ Mutually orthogonal Latin squares with large holes ⋮ Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares ⋮ Mutually orthogonal rectangular gerechte designs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of incomplete transversal designs with block size five and any index \(\lambda\)
• Four MOLS of orders 20, 30, 38, and 44
• Four MOLS of order 10 with a hole of order 2
• On sets of three mols with holes
• Subplanes of the Hughes plane of order 25
• On the existence of MOLS with equal-sized holes
• Existence of three HMOLS of types \(h^ n\) and \(2^ n3^ 1\)
• An elliptic semiplane
• New Wilson-type constructions of mutually orthogonal latin squares
• A series of separable designs with application to pairwise orthogonal Latin squares
• More mutually orthogonal latin squares
• Four mutually orthogonal Latin squares of orders \(28\) and \(52\)
• Sets of mutually orthogonal Latin squares with ``like subsquares
• Constructions of perfect Mendelsohn designs
• Combinatorial theory seminar Eindhoven University of Technology
• On seven mutually orthogonal latin squares
• On the existence of incomplete transversal designs with block size five
• Sets of mutually orthogonal Latin squares with ``like subsquares. II
• Some direct constructions for incomplete transversal designs
• More thwarts in transversal designs
• \(V (m, t)\)'s for \(m = 4, 5, 6\)
• Transversal designs in classical planes and spaces
• Thwarts in transversal designs
• The spectrum of \(\text{HSOLSSOM}(h^ n)\) where \(h\) is even
• Finite bases for some PBD-closed sets
• Mols with holes
• Concerning the number of mutually orthogonal latin squares
• Five mutually orthogonal latin squares of orders 24 and 40
• A candidate for the ``Next Fermat Problem
• Three mutually orthogonal idempotent Latin squares of orders 22 and 26
• The existence of 3 orthogonal partitioned incomplete Latin squares of type \(t^ n\)
• On some finite non-desarguesian planes
• A Series of Symmetrical Group Divisible Incomplete Block Designs
• Construction of Some Sets of Mutually Orthogonal Latin Squares
• On the Construction of Sets of Mutually Orthogonal Latin Squares and the Falsity of a Conjecture of Euler
• Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler's Conjecture
• On Methods of Constructing Sets of Mutually Orthogonal Latin Squares Using a Computer. I
• Orthomorphisms of Groups and Orthogonal Latin Squares. I
• Nonextendibility Conditions on Mutually Orthogonal Latin Squares
• Some Results on the Existence of Squares
• Five mutually orthogonal Latin squares of order 35
• Finite Projective Planes with Affine Subplanes
• Affine Subplanes of Finite Projective Planes
• Some maximal arcs in finite projective planes
• Blocking Sets in Finite Projective Planes

This page was built for publication: Mutually orthogonal Latin squares: A brief survey of constructions