Projective covering designs

• Main Authors: Chee, Yeow Meng, Ling, San
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Engineering::Computer science and engineering::Mathematics of computing
• Online Access: https://hdl.handle.net/10356/95779; http://hdl.handle.net/10220/9828
• Institution: Nanyang Technological University

A (2, k, v) covering design is a pair (X, F) such that X is a v-element set and F is a family of k-element subsets, called blocks, of X with the property that every pair of distinct elements of X is contained in at least one block. Let C(2, k, v) denote the minimum number of blocks in a (2, k, v) covering design. We construct in this paper a class of (2, k, v) covering designs using number theoretic means, and determine completely the functions C(2,6,6n · 28) for all n ≥ 0, and C(2,6,6n · 28 − 5) for all n ≥ 1. Our covering designs have interesting combinatorial properties.