In the 1970s and 1980s, searches performed by L. Carter, C. Lam, L. Thiel, and S. Swiercz showed that projective planes of order ten with weight 16 codewords do not exist. These searches required highly specialized and optimized computer programs and required about 2,000 hours of computing time on mainframe and supermini computers. In 2011, these searches were verified by D. Roy using an optimized C program and 16,000 hours on a cluster of desktop machines. We performed a verification of these searches by reducing the problem to the Boolean satisfiability problem (SAT). Our verification uses the cube-and-conquer SAT solving paradigm, symmetry breaking techniques using the computer algebra system Maple, and a result of Carter that there are ten nonisomorphic cases to check. Our searches completed in about 30 hours on a desktop machine and produced nonexistence proofs of about 1 terabyte in the DRAT (deletion resolution asymmetric tautology) format.

中文翻译：

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Lam 问题中权重 16 码字的不可满足性证明

在 1970 年代和 1980 年代，L. Carter、C. Lam、L. Thiel 和 S. Swiercz 进行的搜索表明，不存在权重为 16 码字的 10 阶射影平面。这些搜索需要高度专业化和优化的计算机程序，并且在大型机和超小型计算机上需要大约 2,000 小时的计算时间。2011 年，D. Roy 使用优化的 C 程序和 16,000 小时在台式机集群上验证了这些搜索。我们通过将问题简化为布尔可满足性问题 (SAT) 来验证这些搜索。我们的验证使用cube-and-conquer SAT求解范式，使用计算机代数系统Maple的对称破坏技术，以及Carter的结果，有十个非同构情况需要检查。