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I think that Quilodran's Quilodrán's solution to the joints problem in $\mathbb{R}^n$ can be applied to the finite field case, to get the same bounds. This is the paper, "The joints problem in $\mathbb{R}^n$": Abstract: http://arxiv.org/pdf/0906.0555.pdfarXiv:0906.0555v3; PDF link. |
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I think that Quilodran's solution to the joints problem in $\mathbb{R}^n$ can be applied to the finite field case, to get the same bounds. This is the paper: |
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