Two size-4 Sidon sets {0,1,3,11} and {0,1,4,11} and their dilations fail to extend to perfect difference sets for all checked moduli up to 133 and prime powers up to 317.
Independent brute-force verification of 4 candidate non-extending size-4 Sidon sets:\n
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Size-4 Counterexamples to the Sidon-Extension Conjecture
Two size-4 Sidon sets {0,1,3,11} and {0,1,4,11} and their dilations fail to extend to perfect difference sets for all checked moduli up to 133 and prime powers up to 317.