Journal of Geometry

, Volume 13, Issue 2, pp 210–216 | Cite as

Partial t-spreads and group constructible (s,r,μ)-nets

  • David A. Drake
  • J. W. Freeman


We give a method for constructing (s,r,μ)-nets out of partial t-spreads. As one consequence, we are able to apply a theorem of Bose and Bush to improve the known upper bound for the number of subspaces in a partial t-spread. Conversely, known existence results for partial t-spreads yield (s,r,μ)-nets with large replication number r.


Existence Result Replication Number Group Constructible Large Replication 
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  1. [1]
    Beutelspacher, Albrecht: Partial spreads in finite projective spaces and partial designs. Math. Zeit. 145 (1975), 211–229.CrossRefGoogle Scholar
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    Bose, R. C. and Bush, K. A.: Orthogonal arrays of strength two and three. Annals of Math. Stat. 23 (1952), 508–524.Google Scholar
  3. [3]
    Drake, David A.: Partial λ-geometries and generalized Hadamard matrices over groups. Canadian J., to appear.Google Scholar
  4. [4]
    Drake, David A. and Jungnickel, Dieter: Klingenberg structures and partial designs II: regularity and uniformity. Pacific J., to appear.Google Scholar

Copyright information

© Birkhäuser Verlag 1979

Authors and Affiliations

  • David A. Drake
    • 1
  • J. W. Freeman
    • 2
  1. 1.University of FloridaGainesville
  2. 2.Virginia Commonwealth Univ.Richmond

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