We have developed a new technique for generating homogeneously distributed irregular dot patterns useful for optical devices and digital halftoning technologies. To introduce irregularity, we use elaborately designed sequences called low-discrepancy sequences instead of pseudorandom numbers. We also use a molecular-dynamics redistribution method to improve the distribution of dots. Our method can produce arbitrary density distributions in accordance with a given design. The generated patterns are free from visible roughness as well as any moiré patterns when superimposed on other regular patterns. We demonstrate that our method effectively improves luminance uniformity and eliminates moiré patterns when used for a backlight unit of a liquid-crystal display.