Concerning the number of mutually orthogonal latin squares

DOI10.1016/0012-365X(74)90148-4zbMath0283.05009OpenAlexW2001496048WikidataQ106165109 ScholiaQ106165109MaRDI QIDQ1844237

Publication date: 1974

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(74)90148-4

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Orthogonal arrays, Latin squares, Room squares (05B15)

Related Items

On \(\lambda\)-covers of pairs by quintuples: \(v\) odd ⋮ Sharp sets of permutations ⋮ 2-perfect directed \(m\)-cycle systems can be equationally defined for \(m=3,4\), and \(5\) only ⋮ \(2\)-perfect \(m\)-cycle systems can be equationally defined for \(m=3\), \(5\), and \(7\) only ⋮ A candidate for the ``Next Fermat Problem ⋮ Pairwise balanced designs with block sizes \(6t+1\) ⋮ Coverings pairs by quintuples: The case v congruent to 3 (mod 4) ⋮ Automorphism subgroups for designs with \(\lambda =1\) ⋮ Packing arrays ⋮ Exact coverings of 2-paths by 4-cycles ⋮ Halving Steiner 2-designs ⋮ Unnamed Item ⋮ The optimal bound on the 3-independence number obtainable from a polynomial-type method ⋮ New Wilson-type constructions of mutually orthogonal latin squares ⋮ A short disproof of Euler's conjecture based on quasi-difference matrices and difference matrices ⋮ A general construction for group-divisible designs ⋮ Percentages in pairwise balanced designs ⋮ Subspaces of linear spaces of line size 4 ⋮ Pairwise balanced designs with odd block sizes exceeding five ⋮ Further results on incomplete (3,2,1)-conjugate orthogonal idempotent Latin squares ⋮ The spectrum of room cubes ⋮ Four mutually orthogonal Latin squares of orders \(28\) and \(52\) ⋮ Constructions of perfect Mendelsohn designs ⋮ Towards the spectrum of Room squares with subsquares ⋮ Enumerating extensions of mutually orthogonal Latin squares ⋮ Existence results for generalized balanced tournament designs with block size 3 ⋮ Holey Steiner pentagon systems and related designs ⋮ Mutually orthogonal Latin squares: A brief survey of constructions ⋮ On the spectrum of resolvable orthogonal arrays invariant under the Klein group \(K_ 4\) ⋮ Ovals and hyperovals in nets ⋮ Varieties of algebras arising from \(K\)-perfect \(m\)-cycle systems ⋮ Balanced incomplete block designs and related designs ⋮ Resolvable group divisible designs with large groups ⋮ A lower bound on permutation codes of distance \(n-1\) ⋮ On seven mutually orthogonal latin squares ⋮ A lower bound on HMOLS with equal sized holes ⋮ Mutually orthogonal Latin squares based on cellular automata ⋮ Conjugate orthogonal quasigroups ⋮ On difference matrices and regular latin squares ⋮ Thwarts in transversal designs ⋮ Embeddings on \(S(2,4,v)\) ⋮ The spectra of a variety of quasigroups and related combinatorial designs ⋮ Finite bases for some PBD-closed sets ⋮ Unnamed Item ⋮ Eine Bemerkung zur Abschätzung der Anzahl orthogonaler lateinischer Quadrate mittels Siebverfahren ⋮ The spectrum of Room cubes ⋮ Resolvable BIBD and SOLS ⋮ On group divisible covering designs ⋮ Existence of holey 3-GDDs of type \((u,g^t w^1)\) ⋮ Doubly diagonal orthogonal Latin squares ⋮ Mutually orthogonal Latin squares with large holes ⋮ Constructions of Nested Orthogonal Arrays ⋮ Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares ⋮ Existence of resolvable BIBDs with \(k=5\) and \(\lambda=4\)

Cites Work