In an answer to this question, someone cites this federal law:
[2 U.S. Code § 2c] - Number of Congressional Districts; number of Representatives from each District
In each State entitled in the Ninety-first Congress or in any subsequent Congress thereafter to more than one Representative under an apportionment made pursuant to the provisions of section 2a(a) of this title, there shall be established by law a number of districts equal to the number of Representatives to which such State is so entitled, and Representatives shall be elected only from districts so established, no district to elect more than one Representative (except that a State which is entitled to more than one Representative and which has in all previous elections elected its Representatives at Large may elect its Representatives at Large to the Ninety-first Congress).
Suppose a state is entitled to eight representatives in Congress, and the constitution of the state says every voter throughout the whole state gets the same ballot listing the same candidates and can vote for as many as the voter chooses. Thus if 30 candidates for the eight seats on the ballot you could vote for two of them or 15 of them, etc., and the eight with the most votes are elected.
Obviously this would eliminate gerrymandering.
But it conflicts with a federal statute.
It is considered permissible for a state legislature to decide that the governor will appoint all of the presidential electors, or the legislature will do so, or a different elector in each of several districts will be elected (Maine and Nebraska do that, so their electors do not always vote unanimously) or to either permit or forbid "faithless electors" (Washington allows them but makes them pay a fine; Minnesota says they are out of order and replaces them on the spot with someone else,...), and this mode of at-large election of representatives seems reasonable by comparison.
If a state constitution provided for this method of election, and someone challenged it in federal court because of that statute, would the statute survive?