Table 1. Properties of k=17, n=2 sequences.

Sequence properties calculated for a single, path-guided de Bruijn sequence, as well as the best performing of each of 1,000,00 randomly sequences of each type. The random de Bruijn sequences were generated from random Hamiltonian circuit; the type 1 index 1 and m-sequences were produced by searching across permutations of the assignment of labels to stimuli. DP_rel-adapt calculated by taking the variance of the hypothesized neural modulation proportional to sequential stimulus distance as the denominator, and the numerator as the variance of that modulation following application of a 0.01 Hz high-pass notch filter and convolution with a hemodynamic response function (Aguirre et al 1998). DP_rel-main was calculated for the main (direct) effect of presentation of any of the 16 stimuli versus the null-trials. Autocorrelation is the square root of the SSQ of the correlation of a sequence with itself at every lag except zero. Balance is a measure of the even distribution of labels across the sequence; small numbers indicate more balance (Hsieh et al 2004). Uniformity is a measure of spacing of labels across the sequence; small numbers indicate a more uniform distribution of labels (Hsieh et al 2004).

Sequence	DPrel-adapt	DPrel-main	Autocorrelation	Balance	Uniformity
path-guided de Bruijn	0.74	0.31	1.09	1918	95
random de Bruijn	0.29	0.34	0.99	1309	96
type 1, index 1	0.28	0.34	1.03	293	26
m-sequence	0.32	0.32	1.22	1135	94