Discrepancy
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Points too even to be random
Independent random points clump, and the clumping is what makes the error fall only as the square root. Points chosen to be evenly spread rather than independently beat that rate, and the price is that nothing about them is random at all.
Points on a lattice that see almost nothing
Average a function over the points of a carefully tilted lattice and the error can fall like one over the square of the number of points — far faster than random sampling, and faster than the most evenly spread sequences. The reason is that a lattice rule is blind to only a thin set of frequencies, its dual lattice, and a smooth periodic function has almost nothing there.
Named alongside it
The objects these essays reach for when they reach for this one.
Convergence rateDual latticeEquidistributionError boundFourier seriesIntegralLatticeMonte CarloNumerical integrationPeriodicityPseudorandomnessQuasi-monte carlo