Transitive PSL(2,7)-invariant 42-arcs in 3-dimensional projective spaces

摘要

We construct an infinite family of transitive 42-arcs in PG(3, q~2), with q = p~n ≥ 29 and q ≡ 1 (mod 7), under the action of the group PSL(2, 7) in its representation as a subgroup of PGL(4, q). Further, we study the case q = 29 in detail with computer assistance. For q - 29 these 42-arcs turn out to be complete.