The　balanced　hypercube　BHn　plays　an　essential　role　in　large-scale　parallel　and　distributed　computing　systems.　With　the　increasing　probability　of　edge　faults　in　large-scale　networks　and　the　widespread　applications　of　Hamiltonian　paths　and　cycles,　it　is　especially　essential　to　study　the　fault　tolerance　of　networks　in　the　presence　of　Hamiltonian　paths　and　cycles.　However,　existing　researches　on　edge　faults　ignore　that　it　is　almost　impossible　for　all　faulty　edges　to　be　concentrated　in　a　certain　dimension.　Thus,　the　fault　tolerance　performance　of　interconnection　networks　is　severely　underestimated.　This　paper　focuses　on　three　measures,　t-partition-edge　fault-tolerant　Hamiltonian,　t-partition-edge　fault-tolerant　Hamiltonian　laceable,　and　t-partition-edge　fault-tolerant　strongly　Hamiltonian　laceable,　and　utilizes　these　measures　to　explore　the　existence　of　Hamiltonian　paths　and　cycles　in　balanced　hypercubes　with　exponentially　faulty　edges.　We　show　that　the　BHn　is　2n−1-partition-edge　fault-tolerant　Hamiltonian　laceable,　2n−1-partition-edge　fault-tolerant　Hamiltonian,　and　(2n−1−1)-partition-edge　fault-tolerant　strongly　Hamiltonian　laceable　for　n≥2.　Comparison　results　show　the　partitioned　fault　model　can　provide　the　exponential　fault　tolerance　as　the　value　of　the　dimension　n　grows.　©　2023　Elsevier　Inc.