Table 1.
k | 2 | 4 | 6 | 8 | 10 | 12 | 14 |
---|---|---|---|---|---|---|---|
Original | 16 | 256 | 4096 | 65 536 | 1 048 576 | 16 777 216 | 268 435 456 |
Lower bound | 10 | 136 | 2080 | 32 896 | 524 800 | 8 390 656 | 134 225 920 |
Algorithm 1 | 10 | 142 | 2140 | 33 262 | 526 840 | 8 400 808 | 134 275 060 |
Optimal | 10 | 142 | 2140 | 33 262 | 526 816 | 8 400 772 | 134 274 844 |
Saving factor | 1.6 | 1.8 | 1.91 | 1.97 | 1.990 | 1.997 | 1.999 |
Note: The top row is the length of a regular de Bruijn sequence that does not exploit complementarity. The next row contains the theoretical lower bound on RC complete sequence length (Proposition 1). The next two rows are the lengths of the sequence computed by the two algorithms of Section 3.3.1 and 3.3.2. The saving factor is the ratio between the original sequence length and length of the optimal RC complete sequence. Note that the lower bound is not tight.