New upper bounds for covering arrays of strength 3 and 4
Year: 2026
Type: preprint
Abstract: We give explicit covering arrays that improve the best known size for 77 parameter sets: 19 of strength 3, 50 of strength 4 and 8 of strength 5. Examples are CA(2976;4,12,6) (previously 3944), CA(2976;4,11,6) (previously 3671), CA(2616;4,10,6) (previously 3208) and CA(6445;4,37,6) (previously 7199). The arrays come from unions of orbits of PGL(2,q) and its subgroups followed by row-level repair, from a family developed under PGL(2,5) on the symbols and a cyclic shift of the columns, from unions of cosets of linear codes, from search programs written by a large language model inside an automated loop, and from post-optimisation of published record arrays. Every array is its own certificate; all were checked exhaustively by two separately written programs and are archived with their generating programs. We report what the language model did and did not contribute, including a baseline without it and a pre-registered prediction that failed. Version 1.3 adds the 46 arrays of version 1.7 of the archive (doi:10.5281/zenodo.23959429): 33 new parameter sets and 13 improvements of our own entries, among them the line CA(N;4,k,6) for k = 28 to 39 and four entries taken back from the deposit of Bai XunDi. Nine of the new sets (k = 28 to 36) are column deletions of the single array CA(6445;4,37,6), and 22 come from post-optimisation of published arrays, mostly those of Bai XunDi, with small gains. Version 1.1 corrected version 1.0, which claimed 39 parameter sets: eight of them had already been overtaken by a deposit of Bai XunDi, credited here.
Author: Sitjar, Théo Nicolas
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225004616