“根据法律执行的”可以翻译为 “executed in accordance with the law” 或者 “carried out in compliance with the law”。
例句：
These measures must be executed in accordance with the law.（这些措施必须根据法律执行。）
All administrative actions should be carried out in compliance with the law.（所有行政行为都应当根据法律执行 。）