- Full text PDF available (6)
The quantity g (k) (v) was introduced in  as the minimum number of blocks necessary in a pairwise balanced design on v elements, subject to the condition that the longest block has length k. Recently, we have needed to use all possibilities for such minimal covering designs, and we record all non-isomorphic solutions to the problem for v ≤ 13.
The minimum number of incomplete blocks required to cover, exactly λ times, all t-element subsets from a set V of cardinality v (v > t) is denoted by g(λ, t; v).
A necessary condition is given for the existence of some Generalised Bhaskar Rao designs (GBRDs) with odd block size over cyclic groups of even order. Some constructions are given for GBRDs over cyclic groups of even order with block size 3 and with block size 4.
A directed triple system of order v, DTS(v), is a pair (V, B) where V is a set of v elements and B is a collection of ordered triples of distinct elements of V with the property that every ordered pair of distinct elements of V occurs in exactly one triple as a subsequence. A set of triples in a DTS(v) D is a defining set for D if it occurs in no other… (More)