Two carpenters are discussing the building codes that apply to balconies. Carpenter A says that according to building codes, a balcony handrail for a public building must be no less than $42"$ high. Carpenter B says that according to codes, a balcony handrail for a home installation must be no less than $40"$ high. Which of the following statements is correct?

A$.$ Only Carpenter $A$ is correct.

B$.$ Neither carpenter is correct.

C$.$ Only Carpenter B is correct.

D$.$ Both carpenters are correct.