  Uncertainty relations and quantum entanglement are pivotal concepts in
quantum theory. Beyond their fundamental significance in shaping our
understanding of the quantum world, they also underpin crucial applications in
quantum information theory. In this article, we investigate entropic
uncertainty relations and entanglement detection with an emphasis on quantum
measurements with design structures. On the one hand, we derive improved
R\'enyi entropic uncertainty relations for design-structured measurements,
exploiting the property that the sum of powered (e.g., squared) probabilities
of obtaining different measurement outcomes is now invariant under unitary
transformations of the measured system and can be easily computed. On the other
hand, the above property essentially imposes a state-independent upper bound,
which is achieved at all pure states, on one's ability to predict local
outcomes when performing a set of design-structured measurements on quantum
systems. Realizing this, we also obtain criteria for detecting multi-partite
entanglement with design-structured measurements.
