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Generating independent Halton sequences in same session

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I would like to create two Halton sequences which should be independent of each other. I use the code below. I am worried that the sequences might be correlated because the seed is the same for borh although I use different Skips and Leaps when creating the two sequences. I tried to use rng(1) and rng(2) before creating each sequence but that turned out to be a naive attempt because in one MATLAB session it is not possible to use different seeds with rng, if I am not mistaken. RandStream seemed to provide a solution but I cannot seem to difure out how I can combine it with the haltonset.
N = 100;
rng default
hal_a = haltonset(N,'Skip',1e3,'Leap',1);
hal_b = haltonset(N,'Skip',2e3,'Leap',2);
hal_a(1:5,1)
hal_b(1:5,1)

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R2021a

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