A new construction for μ-way Steiner trades.

A μ-way (v,k,t) trade T of volume m consists of μ pairwise disjoint collections Ti,...,Tμ, each of m blocks of size k such that for every t-subset of a v-set V, the number of blocks containing this t-subset is the same in each Ti for 1 ≤ i ≤ μ. If any t-subset of the v-set V occurs at most once in each Ti for 1 ≤ i ≤ μ, then T is called a μ-way (v, k, t) Steiner trade. In 2016, it was proved that there exists a 3-way (v, k, 2) Steiner trade of volume m when 12(k - 1) ≤ m for each k. Here we improve the lower bound to 8(k - 1) for even k, by using a recursive construction. [ABSTRACT FROM AUTHOR]