2023/05/23 by Francesco Pavese, Pavese, Francesco · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2305.13838
openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A 4-general set in \rm PG(n,q) is a set of points of \rm PG(n,q) spanning the whole \rm PG(n,q) and such that no four of them are on a plane. Such a pointset is said to be complete if it is not contained in a larger 4-general set of \rm PG(n, q). In this paper upper and lower bounds for the size of the largest and the smallest complete 4-general set in \rm PG(n,q), respectively, are investigated. Complete 4-general sets in \rm PG(n,q), q ∈ \3,4\, whose size is close to the theoretical upper bound are provided. Further results are also presented, including a description of the complete 4-general sets in projective spaces of small dimension over small fields and the construction of a transitive 4-general set of size 3(q + 1) in \rm PG(5, q), q ≡ 1 \pmod3.