A Dataset of Optimal and Perfect Interval Sequences for Chinese Circular Rulers (Cyclic Golomb Rulers): An Independent Discovery up to 158 Intervals

A perfect ruler covers all integers from 1 to the ruler length L, while an optimal ruler covers the maximum possible set of consecutive integers. The author independently discovered and named this concept "Chinese circular ruler" over a decade ago while training students' thinking skills, and later learned that it had been previously studied internationally as "cyclic Golomb ruler." This dataset contains 199 optimal and perfect Chinese circular rulers computed by the author's self-developed program, with the largest number of intervals reaching 158, far exceeding the existing OEIS record of 18 intervals.

Each entry provides the interval sequence, ruler length, and computation time. For certain orders (e.g., 7, 11, 13), perfect rulers are proven nonexistent, and only optimal rulers exist. All data have been verified against the internationally recognized OEIS sequences A004136 (shortest length) and A058241 (number of optimal rulers).