New lower bounds for kissing numbers in dimensions 33 to 39: explicit certificates

Explicit, independently checkable kissing configurations giving new lower bounds τ33 ≥ 370240, τ34 ≥ 390980, τ35 ≥ 415308, τ37 ≥ 499816, τ38 ≥ 605322 and τ39 ≥ 768916 (previous best 364736, 384836, 409676, 498024, 591900 and 763668), and new constant-weight codes A(33,8,8) ≥ 1852, A(34,8,8) ≥ 2013, A(35,8,8) ≥ 2202, A(37,8,8) ≥ 2860, A(38,8,8) ≥ 3088 and A(39,8,8) ≥ 3424. Dimensions 33–35, 37 and 39 use the Edel–Rains–Sloane three-layer construction with the new codes as middle layer. Dimension 38 adds 6855 antipodal pairs of norm-48 Leech vectors to the empty equator of Kravatskiy's 591612-point configuration. The archive contains the certificates and verification programs; every configuration has also been checked by brute force over all pairs in exact integer arithmetic.