On the existence of d-homogeneous 3-way Steiner trades - Amjadi H.; Soltankhah N. (Utilitas Mathematica, 2018)
A μ-way (v, k, t) trade T = {T1, T2,-, Tμ} of volume m consists of fj. disjoint collections T1,T2,...,Tμ}, each of m blocks of size k, such that for every t-subset of v-set V the number of blocks containing this t-subset is the same in each T1 (for 1 ≤ i ≤μ). A μ-way (v, k, t) trade is called μ-way (v, k, t) Steiner trade if any t-subset of found(T) occurs at most once in T1 (Tj, j ≥ 2). A μ-way (v, k, t) trade is called d-homogeneous if each element of V occurs in precisely d blocks of T\ (Tj, j ≥ 2). In this paper we characterize the 3-way 3-homogeneous (v, 3,2) Steiner trades of volume v. Also we show how to construct a 3-way d-homogeneous (v, 3,2) Steiner trade for d {4,5,6}, except for seven small values of v. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.