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**bram kierkels** I want to show that if the t-design $\displaystyle 3-(v,6,1)$, that is the Steinersystem $\displaystyle S(3,6,v)$, exist then $\displaystyle v \equiv_{20} 2$ or $\displaystyle v \equiv_{20}6$.

My first step is to calculate $\displaystyle b_{i} = \lambda \frac{\left(\begin{array}{cc}v-i\\t-i\end{array}\right)}{\left(\begin{array}{cc}k-i\\t-i\end{array}\right)} \forall$ $\displaystyle 0\leq i \leq3$

How can I use these numbers to show that $\displaystyle v \equiv 2$ or $\displaystyle 6$ mod $\displaystyle 20$?

Thanks