Small 3-fold Blocking Sets in PG(2,p^n)

This paper addresses the open problem of constructing small t-fold blocking sets in the finite Desarguesian plane PG(2,p^n), specifically focusing on the case of 3-fold blocking sets. The construction of such sets is important for understanding the structure of finite projective planes and has implications for related combinatorial problems. The paper's contribution lies in providing a construction that achieves the conjectured minimum size for 3-fold blocking sets when n is odd, a previously unsolved problem.

• •The paper constructs 3-fold blocking sets in PG(2,p^n) with a specific size.
• •The construction uses a disjoint union of Rédei type linear blocking sets.
• •The constructed sets lie on the same orbit of a specific projectivity.
• •The result addresses an open problem for odd n.