A Series of BIB Designs

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