files / problems / kissing-5d / compute / q6 / dual_more.json

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{
  "delsarte_deg12": {
    "numerical": 46.336869215638316,
    "trials": [
      {
        "den": 100,
        "certified": false,
        "bound": "927/20",
        "float_bound": 46.35,
        "error": null
      },
      {
        "den": 1000,
        "certified": false,
        "bound": "46337/1000",
        "float_bound": 46.337,
        "error": null
      },
      {
        "den": 10000,
        "certified": false,
        "bound": "463369/10000",
        "float_bound": 46.3369,
        "error": null
      }
    ]
  },
  "delsarte_deg14": {
    "numerical": 46.336869215638316,
    "trials": [
      {
        "den": 1000,
        "certified": false,
        "bound": "46337/1000",
        "float_bound": 46.337,
        "error": null
      },
      {
        "den": 10000,
        "certified": false,
        "bound": "463369/10000",
        "float_bound": 46.3369,
        "error": null
      }
    ]
  },
  "n_certified_ansatz": 51,
  "ansatz_certified": [
    {
      "q": [
        "1",
        "1",
        "2",
        "2"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "630",
      "float_bound": 630.0
    },
    {
      "q": [
        "1",
        "1",
        "3",
        "3"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "140",
      "float_bound": 140.0
    },
    {
      "q": [
        "1",
        "1",
        "3",
        "5/2"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "3375/13",
      "float_bound": 259.61538461538464
    },
    {
      "q": [
        "1",
        "1",
        "3",
        "8/3"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "55545/283",
      "float_bound": 196.27208480565372
    },
    {
      "q": [
        "1",
        "1",
        "5/2",
        "2"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "17745/11",
      "float_bound": 1613.1818181818182
    },
    {
      "q": [
        "1",
        "1",
        "5/2",
        "5/2"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "3430/17",
      "float_bound": 201.76470588235293
    },
    {
      "q": [
        "1",
        "1",
        "8/3",
        "2"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "7000",
      "float_bound": 7000.0
    },
    {
      "q": [
        "1",
        "1",
        "8/3",
        "5/2"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "215",
      "float_bound": 215.0
    },
    {
      "q": [
        "1",
        "1",
        "8/3",
        "8/3"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "1210/7",
      "float_bound": 172.85714285714286
    },
    {
      "q": [
        "1",
        "2",
        "2",
        "0"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "875",
      "float_bound": 875.0
    },
    {
      "q": [
        "1",
        "2",
        "2",
        "1"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "1890/19",
      "float_bound": 99.47368421052632
    },
    {
      "q": [
        "1",
        "2",
        "2",
        "1/2"
      ],
      "deg_q": 3,
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "4235/29",
      "float_bound": 146.0344827586207
    }
  ],
  "comment": "1-point continuum Delsarte cannot go below Odlyzko\u2013Sloane ~46.34.  (t-1/2)q^2 duals that certify sit near 48 or higher.  No certified unrestricted dual below 44.",
  "best_certified": "221991/3733",
  "best_certified_float": 59.4671845700509,
  "best_certified_source": "ansatz_grid",
  "below_44": false
}