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Paper   IPM / M / 149
School of Mathematics
  Title:   On compressing complete designs
1.  G. B. Khosrovshahi
2.  R. Naserasr
  Status:   Published
  Journal: J. Statist. Plann. Inference
  Vol.:  74
  Year:  1998
  Pages:   193-201
  Supported by:  IPM
We call a 2-design D with parameters v,k, and λ = ((v−2) || (k−2)) a complete design. The number of distinct blocks of D, called the support size of D, is denoted by b*. For a complete design with v ≥ 7 and for k=3, Constantine and Hedayat (J. Statist. Plann. Inference 7 (1993), 289-294) have shown that max b*=((v) || 3)−4(v−3), provided a block of D attains the maximum multiplicity, λ. In this paper, we show that if a block of a complete design D with k ≥ 3 is repeated maximum possible times (i.e.,λ = ((v−2) || (k−2))), then b* ≤ ((v) || (k))−k [ ((v−1) || (k−1))−((v−2) || (k−2))−((vk) || (k−1))]− ((v−2) || (k−2))+1. Furthermore, for v=k2k+1, where k−1 is a prime power, and also for v ≡ 1 (mod 12), where k=4, we construct designs for which the equality for b* holds.

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