## Abstract In this paper we give some results on cyclic BIBDs with block size 4. It is proved that a cyclic __B__(4,1;4__^n^ u__) exists where __u__ is a product of primes congruent to 1 modulo 6 and __n__ is a positive integer and __n__ββ₯β3. In the case of __n__β=β2, we also give some partial res
Concerning difference families with block size four
β Scribed by Paul L. Check; Charles J. Colbourn
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 334 KB
- Volume
- 133
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
A direct construction is given for a cyclic difference family of (4p", 4,1)-design for all p E 13 (mod 24) and n 3 0. This corrects in part a construction due to Mathon for prime orders, and extends the construction to prime powers.
π SIMILAR VOLUMES
In this paper, we give constructions of block designs with block size 4 and index 1, for L = 3, 6 which have a blocking set for all admissible orders (with at most 5 possible exceptions). A design which admits a blocking set is 2-colorable. These results, in conjunction with an earlier paper [l], s
## Abstract The object of this paper is the construction of incomplete group divisible designs (IGDDs) with block size four, groupβtype (__g, h__)^__u__^ and index unity. It is shown that the necessary conditions for the existence of such an IGDD are also sufficient with three exceptions and six po
Let M = {m1 , m2 , . . . , m h } and X be a v-set (of points). A holey perfect Mendelsohn designs (briefly (v, k, Ξ») -HPMD), is a triple (X, H, B), where H is a collection of subsets of X (called holes) with sizes M and which partition X, and B is a collection of cyclic k-tuples of X (called blocks)