Construction of non-isomorphic BIBD's by using 2-adjugation technique (Q1820160)

The 2-adjugate mod 2 class of designs has been constructed by \textit{M. N. Vartak} and \textit{G. A. Patwardhan} [J. Comb. Theory, Ser. A 11, 11-26 (1971; Zbl 0228.05012)] for unreduced BIB designs and for symmetrical BIB designs with \(\lambda =1\) by Patwardhan and Vartak. The technique of 2- adjugation has been applied to a design whose incidence matrix has elements (0,-1,1) by Patwardhan et al. Using techniques of \textit{G. A. Patwardhan, P. N. Dandawate} and \textit{M. N. Vartak} [Indian J. Pure Appl. Math. 15, 589-597 (1984)] construct balanced matrices which enable us to obtain some solutions of BIB designs non-isomorphic to those hitherto known and a new series of BTD's and BRD's in the present paper.