Cover the space evenly, one binary bisection per knob.
The same promise as Halton — uniform by construction for
every prefix — paid for elsewhere: Halton reads knob d in base the d-th
prime, so its cover thins as the primes grow, while this reads every knob in
base two and separates them with a set of direction numbers each.
Chosen, and that is the price: a Sobol sequence built on the wrong numbers
does not fail, it covers worse and nobody finds out. These are Joe and Kuo’s
(2008), and a test walks the first dimensions against published values,
because reading a table is not a way of checking it. Past KNOBS
dimensions ask answers None from the first trial rather than quietly in
the middle. Its point is a function of the seed and the index.
The seed, which here shifts the digits rather than drawing them: without
it a Sobol sequence is one fixed sequence and two studies of the same
space would walk it in exactly the same order.