A 59-point configuration for the no-four-in-plane problem in the 28 x 28 x 28 grid (OEIS A280537)

A set of 59 points in the grid {0,...,27}^3 with no four points in a common plane, showing a(28) >= 59 for OEIS A280537 (maximum number of points in an n X n X n grid with no four in a plane). Version 1 of this record gave 58 points; its file is kept. Previous bound: the 2016 Al Zimmermann contest "Non-Coplanar Points" reports 66 points for n = 29; deleting the three outer planes x = 28, y = 28, z = 28 (at most 3 points each) gives a(28) >= 57. As of October 2026 no published value gives more than 57 for n = 28. The configuration is invariant under the rotation (x, y, z) -> (y, z, x): 19 orbits of 3 points plus 2 points on the diagonal x = y = z. Verification: all C(59,4) = 455,126 quadruples have nonzero determinant (verify4.py); an independent check with different code found no three collinear and no four coplanar points. Found by symmetric min-conflicts tabu local search (search_sym.c), written and run with the help of an AI assistant (Claude).