Forget about a ground rod. A single ground rod makes a very poor earth in
any sort of soil except salt water. It is no better than a shallow buried
radial wire of the same length.

You can have a good ground with a relatively small number of shallow buried
radial wires. Begin with 6 or 8 radials about 1/8th or 1/10th wavelengths
long. Then increase number until RECEIVED signal strength from several
stable transmissions stops increasing each time the number is increased by
50%.
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Reg