On compressing complete designs

✍ Scribed by G.B. Khosrovshahi; Reza Naserasr

• Book ID: 104340685
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 129 KB
• Volume: 74
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(98)00089-5

✦ Synopsis

We call a 2-design D with parameters v; k; and =( 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, . In this paper, we show that if a block of a complete design D with k¿3 is repeated maximum possible times (i.e., =(

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.