Packing Designs with Block Size 5 and Indexes 8, 12, 16
نویسندگان
چکیده
A (u, K, 1) packing design of order o, block size K, and index I is a collection of K-element subsets, called blocks of a set V such that every 2-subset of V occurs in at most 1 blocks. The packing problem is to determine the maximum number of blocks in a packing design. In this paper we solve the packing problem with K = 5, 1=8, 12, 16, and all positive integers o with the possible exceptions of (u, A)= (19, 16) (22, 16) (24, 16) (27, 16) (28, 12). c’ 1992 Academic Press, Inc.
منابع مشابه
Packing Designs with Block Size 5 and Index 2: The Case v Even
An (v, •, 2) packing design of order v, block size ~, and index 2 is a collection of ~:-element subsets, called blocks, of a set V such that every 2-subsets of V occurs in at most 2 blocks. The packing problem is to determine the maximum number of blocks in a packing design. In this paper we provide a powerful technique for constructing designs and solve the packing problem in the case tc = 5, ...
متن کاملPacking designs with block size 6 and index 5
Assaf, A.M., A. Hartman and N. Shalaby, Packing designs with block size 6 and index 5, Discrete Mathematics 103 (1992) 121-128. A (v, K, A) packing design of order v, block size K and index 1 is a collection of K-element subsets, called blocks, of a v-set V such that every 2-subset of V occurs in at most I blocks. The packing problem is to determine the maximum number of blocks in a packing des...
متن کاملOn packing designs with block size 5 and indices 3 and 5
Let V be a finite set of order v. A (V,K,A) packing design of index A and block size IC is a collection of K-element subsets, called blocks, such that every 2-subset of V occurs in at most A blocks. The packing problem is to determine the maximum number of blocks, D(V,K,A), in a packing design. It is well known that D(V,K,A) S [-i [:=~ ~]] : : t(VIK,~), where [xl is the largest integer satisfyi...
متن کاملGroup divisible designs with block size four and two groups
We give some constructions of new infinite families of group divisible designs, GDD(n, 2, 4; 1, 2), including one which uses the existence of Bhaskar Rao designs. We show the necessary conditions are sufficient for 3 n 8. For n= 10 there is one missing critical design. If 1> 2, then the necessary conditions are sufficient for n ≡ 4, 5, 8 (mod 12). For each of n=10, 15, 16, 17, 18, 19, and 20 we...
متن کاملGeneralized packing designs
Generalized t-designs, which form a common generalization of objects such as tdesigns, resolvable designs and orthogonal arrays, were defined by Cameron [P.J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835–4842]. In this paper, we define a related class of combinatorial designs which simultaneously generalize packing designs and packing arrays. We describe the sometimes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 59 شماره
صفحات -
تاریخ انتشار 1992