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New Constructions and Necessary Conditions for 4-GDDs With Block Size 5

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  • Dinkayehu M. Woldemariam
  • D. G. Sarvate

Abstract

t-v,k,Λ designs are well-known objects of study. Here, we define t-group divisible designs (t-GDDs) and specifically study t-GDDs, where the number of groups are less than the block size. After a short survey of t-GDDs, we will present some examples of 4-GDDs with block size 5 and two groups and prove that the necessary conditions are sufficient for group sizes 3, 4, 5, 6, 7, 9, and 10. Though the necessary conditions for the existence of t-designs are well known, the actual spectrums for 4-v,5,Λ and for 4-GDD n,2,5;Λ1,Λ2 are obtained as a ready source for researchers interested in the constructions of such designs.

Suggested Citation

  • Dinkayehu M. Woldemariam & D. G. Sarvate, 2025. "New Constructions and Necessary Conditions for 4-GDDs With Block Size 5," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2025, pages 1-9, April.
    • Handle: RePEc:hin:jijmms:8832205
    DOI: 10.1155/ijmm/8832205
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