Using finite geometries to construct 3-PBIB(2) designs and 3-designs (Q1343427)

Several 3-PBIBD's (see \textit{Wei Wandi} and \textit{Yang Benfu} [\(t\)-PBIB designs, Chin. Ann. Math., Ser. B 11, No. 2, 171-178 (1990; Zbl 0708.05004)]) are constructed using geometries on finite fields, mainly taking selected subspaces as treatments and using association schemes linked to dimensions of spanned spaces. The parameters of constructed designs are computed mainly using counting formulas of \textit{Wan Zhexian} [Anzahl theorems in finite singular symplectic, unitary and orthogonal geometries, Discrete Math. 123, No. 1-3, 131-150 (1993; Zbl 0789.05014)]. Interested people can read also papers of Tallini's school.