{
  "id": "regev04-fixed-parameters",
  "categoryId": "svp-provable",
  "paperId": "regev-2004-svp-lecture",
  "date": "2004-12-31",
  "datePrecision": "year",
  "year": 2004,
  "time": {
    "coefficient": 16,
    "expression": "2^{16 n + o(n)}"
  },
  "space": {
    "coefficient": 8,
    "expression": "2^{8 n + o(n)}"
  },
  "tags": [
    "classical",
    "provable",
    "arbitrary lattices"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "Lecture 8 fixes N = 2^{8n} log R₀ and ends by testing all pairs. The displayed 16/8 coefficients normalize this particular fixed-parameter presentation, rather than an optimized AKS bound. Nguyen–Vidick 2008, immediately after Theorem 3.1, explicitly confirms the 16 time coefficient and roughly 2^{8n} points. The course header attributes the lecture to Oded Regev and the scribing to Michael Khanevsky. Only the year is known.",
  "extra": {
    "norm": "Euclidean ℓ₂",
    "success": "Randomized; see the stated source guarantee",
    "model": "Classical; polynomial input-size factors suppressed"
  },
  "evidence": {
    "url": "https://cims.nyu.edu/~regev/teaching/lattices_fall_2004/ln/svpalg.pdf",
    "locator": "PDF p. 1 algorithm, steps 1 and 3; analysis pp. 2–4; NV08 §3 following Theorem 3.1",
    "sourceVersion": "Fall 2004 Lecture 8"
  }
}