An improvement on covering triples by quadruples

作者：Ji L^*

来源：Journal of Combinatorial Designs, 2008, 16(3): 231-243.

DOI：10.1002/jed.20156

• covering design
• candelabra t-system
• H-design frame
• t-wise balanced design
• group divisible t-design

Let C(3, 4, v) be the minimum number of four-element subsets (called blocks or quadruples) of a v-element set X, such that each three-element subset of X is contained in at least one block. Let L(3, 4, v) = [v/4 [v-1/3 [v-2/2]]]. Schiinheim has obtained C(3, 4, v) >= L (3, 4, v). Further, Mills showed that C(3, 4, V) = L (3, 4, v) for v not equivalent to 7 (mod 12), and Hartman, Mills, and Mullin showed that C(3, 4, v) = L(3, 4, v) for v equivalent to 7 (mod 12) with v >= 52423 or v = 499. In this article, it is proved that C(3, 4, v) = L(3, 4, v) for all v = 7 (mod 12) with an exception v = 7 and possible exceptions of v = 12k + 7, k is an element of {1, 2, 39 4, 5, 7, 8, 99 10, 11, 12, 16, 21, 23, 25, 29}.

• 出版日期2008-5
• 单位宿州学院; 苏州大学