On Group-Divisible Designs with Block Size Four and Group-Type gum1

  • Authors:
  • G. Ge;R. S. Rees

  • Affiliations:
  • Department of Mathematics, Suzhou University, Suzhou 215006, P.R. China;Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland A1C 5S7, Canada

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2002

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Abstract

We investigate the spectrum for {4}-GDDs of type gum1. Wedetermine, for each even g, all values of m for which a {4}-GDD of typegum1 exists, for every ‘fourth’ value of u. We similarlydetermine, for each odd g ≠ 11 or 17, all values of m for which a {4}-GDD of typegum1 exists, for every ‘third’ value of u. Finally, weestablish, up to a finite number of values of u, the spectrum for {4}-GDDs of typegum1 where gu is even, g ∉ {11, 17}.