Translation Planes of Small Order

  • Information about the representation of a translation plane
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       Files for Translation Planes of Order 16
       Files for Translation Planes of Order 25
       Files for Translation Planes of Order 27
       Files for Translation Planes of Order 32
       Files for Semifield Planes of Order 32
       Files for Translation Planes of Order 49
       Files for Semifield Planes of Order 81
       Files for Semifield Planes of Order 64
       Files for Semifield Planes of Order 2^8, 5^4 admitting an irreducible planar Baer collineation

    Relevant articles

  • T. Czerwinski, The collineation groups of the translation planes of order 25, Geom. Dedicata 39(1991), 125-137.  
  • U.Dempwolff, C. Charnes, The translation planes of order 49 and their automorphism groups, Math. of Computations 67(1998), 1207-1224.  
  • U.Dempwolff, A. Reifart, The classification of the translation planes of order 16, I, Geom. Dedicata 15(1983), 137-153.  
  • U.Dempwolff, Translation planes of order 27, Designs, Codes and Cryptography 4(1994), 105-121.  
  • U.Dempwolff, Semifield Planes of Order 81, to appear in J. Geometry  
  • U.Dempwolff, A Note on Semifield Planes Admitting Irreducible Planar Baer Collineations, to appear in Osaka J. Math.  
  • R. Mathon, G. Royle, The translation planes of order 49, Designs, Codes and Cryptography 5(1995), 52-72.  
  • R. J. Walker, "Determination of Division Algebras with 32 Elements", Proc. Symp. Appl. Math. XV, Amer. Math. Soc. 1962, pp. 83-85.  
  • Related sites

       Eric Moorhouse: Information about planes of order less than 32
       Gordon Royle: Information about planes of order 16

    Lines of Semifield planes of order 64

  • ZIP Line at infinity, generators of translation group
  • ZIP 80 line pencils