A Series of BIB Designs

Abstract

A series of partially balanced incomplete block design yields under certain
restrictions, a new series of BIB designs with parameters:
$$v=(\genfrac{}{}{0ex}{}{2s+1}{2}),b=\frac{1}{2}(s+1)(\genfrac{}{}{0ex}{}{2s+1}{s+1})$$
$$v=s(\genfrac{}{}{0ex}{}{2s-1}{s}),k=s^2,\lambda =(s-1)(\genfrac{}{}{0ex}{}{2s-1}{s-1})$$
where $s\ge 2$ is any positive integer.