New simple 3-designs on 26 and 28 points (Q2761071)

The paper is about constructions of designs mentioned in the title by means of Driessen's theorem (blocks \(B\) are modified to blocks \((B\cup L)\setminus M\), where \(L \cap B=\emptyset \), \(M\subseteq B\), and the sizes of \(L\) and \(M\) are fixed), and by means of equivalence classes on \(s\)-subsets of \(X\) that are induced by a design on \(X\) (two \(s\)-subsets are equivalent if they yield the same spectrum of intersection sizes with blocks of the design). Starting from \(3\)-\((26,6,1)\) and \(3\)-\((26,8,14)\) designs, the author obtains 16 new 3-designs on 26 points (however, values \(\lambda =280,281\) are probably stated by mistake---the construction seems to yield \(\lambda =260,261\)), and a \(3\)-\((28,9,28)\) design gives 6 new 3-designs on 28 points. Some of the construction steps are based on computer programs.