Vitali sets of full outer measure

Is there a "standard" construction to get a Vitali set in $\mathbb R$ of full outer Lebesgue measure?

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 By "Vitali set" you mean a set of representatives for the equivalence relation "have rational difference"? – Goldstern Jan 29 at 8:08 yes, exactly . – Carlo Mantegazza Jan 29 at 15:20