ON LAMBDA-COVERS OF PAIRS BY QUINTUPLES - UPSILON-ODD

A lambda-cover of pairs by quintuples of a upsilon-set V is a family o f 5-subsets of V (called blocks) with the property that every pair of distinct elements from V occurs in at least lambda blocks. If no other such lambda-cover has fewer blocks, the lambda-cover is said to be mi nimum, and the number of blocks in a minimum lambda-cover is the cover ing number C(lambda)(upsilon, 5, 2), or simply C(lambda)(upsilon). The se numbers are determined here for upsilon = 1 (mod 4), lambda > 1, an d upsilon = 3 (mod 4), lambda greater-than-or-equal-to 1 with the exce ption of upsilon is-an-element-of {53, 63, 73, 83} for lambda = 2. (C) 1994 Academic Press Inc,