{"paper":{"title":"Characterization of matrices $B$ such that $(I,B,B^2)$ generates a digital net with $t$-value zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hiroki Kajiura, Kosuke Suzuki, Makoto Matsumoto","submitted_at":"2018-01-07T07:34:12Z","abstract_excerpt":"We study $3$-dimensional digital nets over $\\mathbb{F}_2$ generated by matrices $(I,B,B^2)$ where $I$ is the identity matrix and $B$ is a square matrix. We give a characterization of $B$ for which the $t$-value of the digital net is $0$. As a corollary, we prove that such $B$ satisfies $B^3=I$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02152","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}