  In this paper, we give a geometric construction of the three strong
non-lifted $(3\mod{5})$-arcs in $\operatorname{PG}(3,5)$ of respective sizes
128, 143, and 168, and construct an infinite family of non-lifted, strong
$(t\mod{q})$-arcs in $\operatorname{PG}(r,q)$ with $t=(q+1)/2$ for all $r\ge3$
and all odd prime powers $q$.
