{
  "scope": "Finite syndrome calculations; not an exhaustive search over bilinear repairs, and not a formal or asymptotic proof.",
  "syndrome_checks": [
    {
      "s": 3,
      "syndromes": 16,
      "ordered_syndrome_pairs": 256,
      "mean_rounding_weight": "11/8",
      "mean_one_variable_defect": "21/8",
      "proved_ratio_lower_expression": "5/21"
    },
    {
      "s": 4,
      "syndromes": 32,
      "ordered_syndrome_pairs": 1024,
      "mean_rounding_weight": "23/16",
      "mean_one_variable_defect": "105/32",
      "proved_ratio_lower_expression": "34/105"
    },
    {
      "s": 5,
      "syndromes": 64,
      "ordered_syndrome_pairs": 4096,
      "mean_rounding_weight": "47/32",
      "mean_one_variable_defect": "465/128",
      "proved_ratio_lower_expression": "196/465"
    },
    {
      "s": 6,
      "syndromes": 128,
      "ordered_syndrome_pairs": 16384,
      "mean_rounding_weight": "95/64",
      "mean_one_variable_defect": "1953/512",
      "proved_ratio_lower_expression": "344/651"
    },
    {
      "s": 7,
      "syndromes": 256,
      "ordered_syndrome_pairs": 65536,
      "mean_rounding_weight": "191/128",
      "mean_one_variable_defect": "8001/2048",
      "proved_ratio_lower_expression": "1712/2667"
    },
    {
      "s": 8,
      "syndromes": 512,
      "ordered_syndrome_pairs": 262144,
      "mean_rounding_weight": "383/256",
      "mean_one_variable_defect": "32385/8192",
      "proved_ratio_lower_expression": "24608/32385"
    }
  ],
  "small_actual_input_case": {
    "s": 3,
    "input_vectors": 256,
    "mean_bilinear_repair_error_per_copy": "1",
    "repair": "One explicit linear syndrome section, not an asserted optimum."
  },
  "not_checked": [
    "all full Reed-Muller repairs",
    "unused-input/evaluation-slice argument",
    "full-rank query realizability",
    "unbounded k inequality",
    "query algorithms"
  ]
}