In more formal language, the discrepancy .

The discrepancy conjecture states that for any sequence of terms and any positive integer , there exists a positive integer such that the finite sequence of the first terms of have discrepancy or greater. Therefore, there is a minimum such that terms of any sequence has a given discrepancy .

In 2014, Boris Konev and Alexei Lisitsa found a 1160-term sequence with discrepancy 2, and showed that all 1161-term sequences have discrepancy 3 [2]. They showed that all known elegant methods for constructing a sequence of that length fail; but one might yet be discovered by brute forcing through all possible sequences, which isn't possible at the moment. They later found a 130000-term sequence with discrepancy 3 [3]. This Demonstration examines those two sequences by providing a plot of the ongoing total for a given multiplier and then an array that highlights the selected terms in red (for ) or blue (for ).

The proof in [1] is an existence proof, and not a constructive proof. The minimum size sequence for forcing discrepancies 3, 4, and up is still unknown.