Completing the spectrum for LGDD (mv)

✍ Scribed by Jian-guo Lei

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 171 KB
• Volume: 5
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/(sici)1520-6610(1997)5:1<1::aid-jcd1>3.0.co;2-j

✦ Synopsis

In this article, we construct LGDD(m v ) for v ≡ 2 (mod 6) and m ≡ 0 (mod 6) by constructing the missing essential values 6 v , v = 8, 14, 26, 50. Thus an LGDD(m v ) exists if and only if v(v -1)m 2 ≡ 0 (mod 6), (v -1)m ≡ 0 (mod 2) and (m, v) = (1, 7). c 1997 John Wiley & Sons, Inc.

is contained in exactly one block.

We usually write GDD(t, k, v; r (t, k, v; v{1}) is denoted by S (t, k, v); it is called Steiner system.

Lemma 1 [1].

There exists an S(3, 6, 26) and there exists an S(3, p + 1, p n + 1) for prime power p and any integer n ≥ 2.

Lemma 2 [7].

There exists a GDD (3, 4, 6v; v{6}) for any integer v ≥ 4.