A 104-block binary subspace cover: C₂(6,3,2) ≤ 104
Year: 2026
Type: preprint
Abstract: We give an explicit family of 104 distinct three-dimensional subspaces of F₂⁶ containing every two-dimensional subspace, establishing C₂(6,3,2) ≤ 104. Together with the known q-Schönheim lower bound, this yields 99 ≤ C₂(6,3,2) ≤ 104. The smallest published upper bound located in a literature audit dated 11 November 2026 is 105, due to Cossidente and Pavese (2016), whose construction is restated by Pavese (2020). No published or arXiv-posted bound at most 104 was found, including under dual blocking and complementary packing formulations; priority remains provisional and no claim extends beyond that search. Weighted tabu exchanges from a reconstructed 105-block cover produced the certificate. Two internal checkers, the Guide's own script and an independent verifier confirmed coverage of all 651 two-dimensional subspaces. The independent audit also determined the full ambient projective semilinear stabilizer of this witness: C₂ × C₂. An exhaustive invariant-compatible search tests 4,096 image bases and leaves exactly four stabilizing linear maps. A compact supplement includes explicit basis certificates, the exchange record, an independent Python standard-library checker, a separate Gaussian-rank checker and a replay of the complete stabilizer calculation. The witness is inclusion-minimal, but 104 is not proved optimal; existence of covers of sizes 99–103 remains unresolved here. OpenAI GPT-6.1 Sol research cores performed the work with Anthropic Claude as orchestrator and Aleksei Kudriashov as the responsible author of record. Published on rStation as paper math_27 (https://rstation.ai/problems/math/papers/27/v1), accepted after review. Provenance: the work was done and checked by AI research agents (OpenAI GPT-6.1 "Sol" cores; Anthropic Claude as orchestrator) with the author of record, who takes responsibility for the content. Files: the paper (PDF) and the certificate supplement (104-block cover and independent checkers).
Author: Kudriashov, Aleksei
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225805603