On classification of 2-(8, 3) and 2-(9, 3) trades (Q2747197)

A \(2\)-\((8,3)\) trade consist in two disjoint collections of 3-subsets of \(\{1,\dots,8\}\) such that for every pair \(A\) in \(\{1,\dots,8\}\), the number of blocks containing \(A\) is the same in both collections. The trade is called Steiner if any pair appears at most once in each collection. The authors provide (up to isomorphism) a complete classification of 2-\((8,3)\) trades. The result produces a total number of 15011 simple 2-\((8,3)\) trades. The method is computational and uses the standard basis for trades. A generalization provides some results on 2-\((9,3)\) trades.