Brainstorming isn't always the best way to produce lots of ideas nor lots of good ideas.
That's because group dynamics often affect how people contribute. A group with low
trust is never going to do well using the standard approach to brainstorming. The way
round this is to use the related technique of Brainwriting. In Brainwriting, the group
don't work as a group, they work individually by writing their ideas down on a sheet of
paper and then take turns in passing these round to others to add to the list. This way,
people can share ideas anonymously and quickly and still come up with a large
quantity of solutions to choose from.