A construction method of a class of SIDS\((n)\) (Q687133)

A double square of order \(n\) is an \(n\times n\) array \(A\), each of whose entries consists of two elements from an \(n\)-set \(S\), such that each element of \(S\) occurs precisely twice in each row and column of \(A\), each 2-subset of \(S\) occurs precisely twice in \(A\), and the main diagonal entries of \(A\) are all of the form \((s,s)\), where \(s\in S\), with each such pair appearing precisely once. A double square is called separable if it can be obtained by superimposing two Latin squares, and it is called inseparable otherwise. A double square \(A\) is called symmetric if \(A\) transpose equals \(A\). The author provides a method for constructing a class of symmetric inseparable double squares of order \(n\), where \(n\equiv 0\) or \(1\pmod 4\) and \(n\geq 16\).