Complement-of-singleton extremizers
= Complement-of-singleton extremizers
The sets $A_i=[m]\setminus\{i\}$ have every $t$-fold intersection of size $m-t$ and every $(t-2)$-fold intersection of size $m-t+2$. For $m\geq t+1$, their common intersection is empty and they attain $m=k+t-2$ in the <constant t-wise intersection dichotomy>.