Infinite families of 2- and 3-designs with parameters v = p + 1, k = (p − 1)/2i + 1, where p odd prime, 2e T (p − 1), e ≥ 2, 1 ≤ i ≤ e

✍ Scribed by Shiro Iwasaki

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 211 KB
• Volume: 5
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/(sici)1520-6610(1997)5:2<95::aid-jcd2>3.0.co;2-s

✦ Synopsis

Let p be an odd prime number such that p -1 = 2 e m for some odd m and e ≥ 2. In this article, by using the special linear fractional group PSL(2, p), for each i, 1 ≤ i ≤ e, except particular cases, we construct a 2-design with parameters v = p + 1, k = (p -1)/2 i + 1 and λ = ((p-1)/2 i +1)(p-1)/2 = k(p-1)/2, and in the case i = e we show that some of these 2-designs are 3-designs. Likewise, by using the linear fractional group PGL(2, p) we construct an infinite family of 3-designs with the same v, k and λ = k(k -2). These supplement a part of [4], in which we gave an infinite family of 3-designs with parameters v = q + 1, k = (q + 1)/2 = (q -1)/2 + 1 and λ = (q + 1)(q -3)/8 = k(k -2)/2, where q is a prime power such that q -1 = 2m for some odd m and q > 7. Some of the designs given in this article and in [4] fill in a few blanks in the table of Chee, Colbourn, and Kreher [2].