Sphere packing in dimension 42
dim 42
Best-known sphere packing in Euclidean dimension 42, as one seat in the Conway–Sloane range 38–43.
PhotoRamaCC BY-SA 2.0 FR
A 2026 paper improves sphere packing in dimensions 39 and 43. It walks 38 through 43 because those are the old Conway–Sloane records. Dimension 42 sits in the middle. The construction did not choose 42. It has not even beaten 1982 there.
What it supports
Sun and Wang, arXiv:2607.20359, August 2026. Antipode construction on cross-sections of the P48 lattices. New records at 39 and 43. Dimensions 40, 41, and 42 reproduce Conway and Sloane 1982. The integer is a seat in a range the authors already planned to walk.
What it does not
Not an exact count of packings. Not a threshold. Not a 42 the lattice prefers. Mathematics happening in dimension 42 is not a 42. Keep this as a refusal, not as a trophy.
Calculation
Dimension 42 is one integer in the interval 38–43. The 2026 paper improves 39 and 43, and restates 40, 41, 42.
Range member. The label is the seat, not an invariant of the packing.
ExactnessMiss / failed
Form42
Unitdimension
Strengthhard
Hung15 September 2026