The spectrum of minimal defining sets of some Steiner systems (Q1861295)

Defining sets of a design were introduced by \textit{K. Gray} [Util. Math. 38, 97-103 (1990; Zbl 0726.05014)] as sets of blocks which are subsets of a unique design; they are said minimal if they properly contain no other defining set. In the paper under review the set of sizes of the minimal defining sets of a design is called its ``spectrum''. The authors investigate the bounds of the spectrum of Steiner systems and, in particular, the case of Steiner triple system of the points and lines of the projective space \(PG(3,2)\); they also point out some open questions concerning the Steiner triple system associated with \(PG(n,2)\) .