Generalizations of Bose's equivalence between complete sets of mutually orthogonal Latin squares and affine planes

DOI10.1016/0097-3165(92)90050-5zbMath0760.05011OpenAlexW2000780261MaRDI QIDQ1194747

Charles F. Laywine, Gary L. Mullen

Publication date: 4 October 1992

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(92)90050-5

zbMATH Keywords

hypercubesorthogonal Latin squaresaffine planesaffine geometriesaffine resolvable designsorthogonal frequency squares

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Finite affine and projective planes (geometric aspects) (51E15) Other designs, configurations (05B30) Orthogonal arrays, Latin squares, Room squares (05B15)

Related Items (9)

Nonisomorphic complete sets of \(F\)-rectangles with prime power dimensions ⋮ \(d\)-dimensional hypercubes and the Euler and MacNeish conjectures ⋮ Construction of the mutually orthogonal extraordinary supersquares ⋮ Unnamed Item ⋮ Point sets with uniformity properties and orthogonal hypercubes ⋮ Subsquares in orthogonal Latin squares as subspaces in affine geometries: A generalization of an equivalence of Bose ⋮ The geometry of frequency squares ⋮ An affine design with v = m2h and k = m2h?1 not equivalent to a complete set of F(mh; mh?1) MOFS ⋮ Orthogonal hypercubes and related designs

Cites Work

• \((s,r;\mu )\)-nets and alternating forms graphs
• Tactical decompositions of designs
• Polynomial representation of complete sets of mutually orthogonal frequency squares of prime power order
• Orthogonal arrays with variable numbers of symbols
• Further contributions to the theory of F-squares design
• Affine resolvable balanced incomplete block designs: a survey
• Optimal designs for the elimination of multi-way heterogeneity
• A counter-example to a conjecture relating complete sets of frequency squares and affine geometries
• Subfield permutation polynomials and orthogonal subfield systems in finite fields
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