a new construction for µ-way steiner trades

A mu -way (v,k,t) trade t of volume m consists of mu pairwise disjoint collections t1... ,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 t_i for 1≤ i≤ mu . if any t -subset of the v -set v occurs at most once in each t_i for 1≤ i≤ mu , then t is called a mu -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.