11. An elementary construction using hypocycloids was found by achieving the same lower bound . 12. The program aims at utilizing these symmetries for proving lower bounds . 13. In particular, David S . Johnson obtained a lower bound by computer experiment: 14. The result is related to a linear lower bound for the Hermite constant. 15. These are lower bounds ; the typical frequency is expected to be much higher. 16. The maximum density is a lower bound on the height of the channel. 17. Theoretically, exponential lower bounds have been proved for the DPLL family of algorithms. 18. A bound of type LO means a lower bound is applied. 19. For others investigations have determined upper and lower bounds , but not exact solutions. 20. Lower bounds for multiplication are also known for some classes of branching programs.
