How Many Code and Test Cases Are Enough? Evaluating Test Cases Generation from a Binary-Matrix Perspective

Evaluating test cases automatically generated by Large Language Models (LLMs) is a critical yet challenging task. Existing benchmarks suffer from high computational costs, score inflation, and a bias towards trivial bugs over rare, critical faults. In this work, we ask two fundamental questions: (1) What is the minimal set of wrong codes sufficient to represent the entire error space? and (2) What is the minimal set of test cases needed to distinguish them? We introduce a framework that formalizes benchmark construction as finding an optimal diagnostic basis in a binary code-test matrix. The rank of this matrix specifies the minimal number of independent error patterns (wrong codes) and provides a tight upper bound on the number of test cases required for complete fault coverage. Our objective is to identify a basis of size equal to the matrix rank that maximizes internal diversity. To tackle this NP-hard problem, we propose WrongSelect, an efficient approximation algorithm to select maximally diverse wrong codes. Applying this framework to millions of competitive programming submissions, we construct TC-Bench, a compact, diverse, and inflation-resistant benchmark. Extensive experiments show that even the most advanced test case generation methods achieve only ~60% exclusion rates on TC-Bench, exposing a significant gap in their diagnostic power. Our dataset is available at:this https URLand our code is at:this https URL.