files / problems / kissing-5d / compute / certs / restricted_delsarte.json

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{
  "D5_inner_products": {
    "comment": "Delsarte dual for spherical codes in S^4 whose distinct inner products lie in {-1,-1/2,0,1/2}. f(1)/f_0 = 42 excludes sizes 43 and 44 in this class. The root-system argument in RESEARCH.md then cuts the same class to 40.",
    "T": ["-1", "-1/2", "0", "1/2"],
    "gegenbauer_coeffs": ["1", "49/45", "28/3", "0", "32/3", "896/45"],
    "bound": "42"
  },
  "L5_inner_products": {
    "comment": "Delsarte dual for inner products in {-1,-3/4,-1/2,-1/4,0,1/2}, the exact angle set of Leech's L5. f(1)/f_0 = 239925/5456 < 44 excludes size 44 in this class.",
    "T": ["-1", "-3/4", "-1/2", "-1/4", "0", "1/2"],
    "gegenbauer_coeffs": ["1", "169541/45136", "28/3", "6095/651", "32/3", "0", "0", "0", "0", "131072/13299"],
    "bound": "239925/5456"
  }
}