Large-table semantic annotation aims to assign ontology-grounded semantic labels to columns and column pairs in large relational tables, while considering the efficiency bottleneck caused by the increasing scale of table contexts. However, as relational tables continue to grow in scale, existing methods face a critical effectiveness–efficiency trade-off: directly modeling the full table preserves rich context but introduces substantial computational overhead, while aggressive filtering may discard useful semantic cues. To address this issue, we propose TRACER, an information entropy-grounded framework for efficient large-table semantic annotation. TRACER ranks table rows according to ontology-related semantic uncertainty and constructs compact evidence-oriented contexts through hybrid compression, enabling a lightweight semantic reader to perform column type and column property annotation efficiently. From an information-theoretic perspective, TRACER formulates large-table compression as a conditional entropy minimization problem, providing a principled basis for preserving key semantic evidence while filtering redundant information. Experiments on several benchmarks show that TRACER achieves a strong balance between annotation effectiveness and inference efficiency compared with task-specific and large language model baselines. The source code and data are available at https://anonymous.4open.science/r/TRACER-4884.