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Journal of Geometry

, 109:5 | Cite as

The number of different reduced complete sets of MOLS corresponding to PG \(\varvec{(2,q)}\)

  • K. H. Hicks
  • G. L. Mullen
  • L. Storme
  • J. Vanpoucke
Article
First Online:
Received:
Revised:

Abstract

In the first part of this article we determine the exact number of different reduced complete sets of mutually orthogonal latin squares (MOLS) of order q, for \(q = p^d\), p prime, \(d \ge 1\), corresponding to the Desarguesian projective planes PG(2, q). In the second part we provide some computational results and enumerate the maximal sets of reduced latin squares of order n as part of a set containing exactly r MOLS.

Keywords

Computations Desarguesian projective planes latin squares mutually orthogonal latin squares 

Mathematics Subject Classification

05B15 05B25 51E15 
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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsOhio UniversityAthensUSA
  2. 2.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA
  3. 3.Department of MathematicsGhent UniversityGhentBelgium
  4. 4.Department of Mathematics, Faculty of EngineeringVrije Universiteit BrusselBrusselsBelgium

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