This page lists some results obtained by running the program. There were a number of errors in appendix 3 of the article in CREGJ 118, which are corrected in this table, and in the text that follows the table.
Apart from the final column, this table is populated when this page is loaded, via a Javascript program that is based on the discussion in appendix 3 of the article in CREGJ 118 – function populateTableWithNecklaceResults(). (Using JS to populate the table is mainly just to avoid a lot of tedious typing). The final column has been manually added after running the demonstration program.
Go to landing page | Demonstration | Results commentary
Predicted Necklace Codes, C is shown relative to the total number of
codes of length N, which is 2^N of course. Bad codes is
2^N – C. The prediction for bad codes is explained in appendix 3 of
the article in CREGJ 118 and is based on the number of factors of N. In all cases,
the prediction matches the number of necklace codes found by the demonstration program.
The necklace codes can be assembled into C/N Predicted Necklaces.
Not all of those can be used to assemble a Gray code sequence because sequences must use an even
number of necklaces. Thus the length of the Predicted Max Sequence might be less than
Predicted Necklace Codes. Addditionally, it is not always possible to use all of the
necklace codes so the Actual Max Sequence found by the demonstration program might be lower
still.
| N | Predicted Necklace Codes | Bad codes | ∴ Predicted Necklaces | ∴ Predicted Max Sequence | Actual Max Sequence |
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| replace via JS | 20 | ||||
| replace via JS | 21 | Last row |
corrections here
/pub/cregj/more/j118/gray_code_results.html, last modified Tue, 27 Sep 2022 16:13:41 +0100. Server: britiac4.british-caving.org.uk (31.25.186.126)