Well, no fixed criteria in statistics. Yes, there exist many theories and methodologies to create random sequences or numbers. However, this will depend on the population nature, situations and surrounding environment.
In general, we may think like following:
- Many persons/machines to share in sample selection is better than to be done by only one. Diversity leads to better randomness.
- Selecting in different times/situations/places is better than to do at once in order to get more randomness.
- Changing methodologies/media of selection may help.
- Combining two or more random samples create better random sample.
Anyway, since our goal is to get accurate inferences, we should try as possible to be randomized in sample selection.