| n\d | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 1 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 9 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 3 | 27 | 9 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 4 | 81 | 27 | 7 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 5 | 243 | 81 | 15 | 5 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 6 | 729 | 243 | 35-36 | 13 | 4 | 3 | 1 | 1 | 1 | 1 | 1 | 1 |
| 7 | 2187 | 729 | 71-108 | 21-24 | 8 | 3 | 3 | 1 | 1 | 1 | 1 | 1 |
| 8 | 6561 | 2187 | 179-324 | 41-72 | 15-24 | 7 | 3 | 3 | 1 | 1 | 1 | 1 |
| 9 | 19683 | 6561 | 438-937 | 88-216 | 25-72 | 12-18 | 6 | 3 | 3 | 1 | 1 | 1 |
| 10 | 59049 | 19683 | 1133-2811 | 202-648 | 49-216 | 18-54 | 9-14 | 5 | 3 | 3 | 1 | 1 |
| 11 | 177147 | 59049 | 2972-7029 | 471-1944 | 98-648 | 29-162 | 11-36 | 7-12 | 4 | 3 | 3 | 1 |
| 12 | 531441 | 177147 | 7819-19683 | 1129-5832 | 208-1557 | 56-486 | 20-108 | 10-36 | 7-9 | 4 | 3 | 3 |
The above table shows E3(n,d), the number of codewords in an optimal ternary code of fixed length n and minimum edit distance d. Where exact values are not known, upper and lower bounds are provided.
The earliest version of this table appeared in the technical report: S.K.Houghten, D.Ashlock and J.Lenarz, "Bounds on Optimal Edit-Metric Codes"and was ultimately published as "Construction of Optimal Edit Metric Codes", Proceedings of the 2006 IEEE Workshop on Information Theory (ITW 2006), 259-263.
Improvements since that time:
If you have improvements, comments, etc, please e-mail shoughten@brocku.ca
This page last modified 22nd August 2005 © Copyright Sheridan Houghten, 2005