the exact details of the design ideas (specified)

See: specification, design.

Can be taken to mean the same as a Requirments Specification. Sommerville considers this to be a detailed abstract description which is the basis for the system design. Based on Sommerville, Software Engineering

A specification setting forth the required characteristics to be considered for award of contract, including sufficient detail to show how the product is to be manufactured.

specification that documents the design of a system or system component; for example, a software configuration item. Typical contents include system or component algorithms, control logic, data structures, data set-use information, input/output formats and interface descriptions. See requirements specifications.

NIST] A specification that documents how a system is to be built. It typically includes system or component structure, algorithms, control logic, data structures, data set [file] use information, input/output formats, interface descriptions, etc Contrast with design standards, requirement.

A document specifying the test conditions (coverage items) for a test item, the detailed test approach and identifying the associated high level test cases.

Design specifications are the measurements and characteristics of a structure or object which provide for a workable, sustainable, or pleasing creation or construct. This can apply to a wide variety of manufactured or fabricated objects, such as buildings, automobiles, and clothes and also utility, computing, and distribution systems. Any functional thing made by human beings has certain specific details.