On the maximal number of factors and the enumeration of 3-symbol orthogonal arrays of strength 3 and index 2
An \(s\)-symbol orthogonal array of strength \(t,\) index \(\lambda\) and \(k\) factors is a \((k,\lambda s^t)\)-matrix with entries from an \(s\)-element set such that any \(t\) rows contain each \(t\)-tuple of entries exactly \(\lambda\) times. Denote this structure by \(\text{OA}_{\lambda}(t,k,s)\). The paper presents purely combinatorial proofs of the following facts: (1) There are exactly four essentially different \(\text{OA}_2(3,5,3)\). (2) There is no \(\text{OA}_2(3,6,3)\). (3) There is exactly one \(\text{OA}_3(2,5,2)\) without a repeated column.
scientific article; zbMATH DE number 1040400