{
  "$type": "site.standard.document",
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  "path": "/report/2026/072",
  "publishedAt": "2026-05-10T14:19:55.000Z",
  "site": "https://eccc.weizmann.ac.il",
  "textContent": "We study the question of explicitly constructing variety-evasive subspace families, a pseudorandom primitive introduced by Guo (Computational Complexity 2024) that generalizes both hitting sets and lossless rank condensers. Roughly speaking, a variety-evasive subspace family $\\mathcal{H}$ is a collection of subspaces such that for every algebraic variety $V$ in a fixed family $\\mathcal{F}$, there is some subspace $W \\in \\mathcal{H}$ that is in general position with respect to $V$. We give an explicit construction of a subspace families that evade all degree-$d$ varieties in an $n$-dimensional affine or projective space. Our construction improves on the size of the variety-evasive subspace families constructed by Guo and, for varieties of degree $n^{1 + \\Omega(1)}$, comes within a polynomial factor of Guo's lower bound on the size of any such variety-evasive subspace family. Our variety-evasive subspace families rely on an improved construction of hitting sets for Chow forms of algebraic varieties.",
  "title": "TR26-072 |  An Improved Construction of Variety-Evasive Subspace Families | \n\n\tRobert Andrews, \n\n\tAbhibhav Garg"
}