2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75544The cohomology on the complement of hyperplanes with the coefficients in the rank one local system associated to a generic weight vanishes except in the highest dimension. In this paper, we construct matroids or arrangements and its weights with non-vanishing cohomology of Orlik-Solomon algebras, using decomposable relations arising from Latin hypercubes.13 pages, 7 figuresCombinatoricsAlgebraic Topology52C35; 32S22, 14F99text