Asymptotic Bounds for General Covering Designs

作者：Montecalvo Federico^*

来源：Journal of Combinatorial Designs, 2015, 23(1): 18-44.

DOI：10.1002/jcd.21401

• asymptotic covering density
• covering design
• lotto design
• Turan density
• Turan system

Given five positive integers n,p,k,, and t where nkt and npt, a t-(n,k,p,)general covering design is a pair (X,B) where X is a set of n elements (called points) and B a multiset of k-subsets of X (called blocks) such that every p-subset of X intersects at least blocks of B in at least t points. In this article we continue the work carried out by Etzion, Wei, and Zhang [Des. Codes Cryptogr. 5 (1995), 217-239] on the asymptotic covering density of general covering designs. We will present combinatorial constructions leading to new upper bounds on the asymptotic covering density of 4-(n, 4, 6, 1) general covering designs and 4-(n,5,p,1) general covering designs with 5p6. The new bound on the asymptotic covering density of 4-(n, 4, 6, 1) general covering designs is equivalent to a new lower bound for the Turan density pi(K-6(4)).

• 出版日期2015-1