Hadwiger covering / illumination number in $\mathbb{R}^3$ (39a)

Hadwiger covering / illumination number in $\mathbb{R}^3$

39a

Upper bound, last-listed row

| $14$ | [Pry2023] | Best known general upper bound: $H_3 \le 14$ (attributed to Prymak). [ABP2024-ub-H3-14] |

exact pinned row

| $14$ | <a href="#Pry2023">[Pry2023]</a> | Best known general upper bound: $H_3 \le 14$ (attributed to Prymak). <a href="#ABP2024-ub-H3-14">[ABP2024-ub-H3-14]</a> |

tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $8$ | Classical (cube) | $H_3 \ge 2^3 = 8$ (already forced by the cube / parallelotope). [ABP2024-lb-cube] |

exact pinned row

| $8$ | Classical (cube) | $H_3 \ge 2^3 = 8$ (already forced by the cube / parallelotope). <a href="#ABP2024-lb-cube">[ABP2024-lb-cube]</a> |

tracked since 2026-07-24 — no movement seen yet

Cite this row

Bounds Ledger — Hadwiger covering / illumination number in $\mathbb{R}^3$ (39a)
upper bound: $14$ (tracked since 2026-07-24 — no movement seen yet)
lower bound: $8$ (tracked since 2026-07-24 — no movement seen yet)
Mirrored from teorth/optimizationproblems@2c1968c. These are the last-listed rows of that constant's bounds table — a listing position, not a statement that this bound is the strongest or most recent. A snapshot at that sha, not a live read.
https://u00dxk2.github.io/bounds-ledger/c/39a.html