Yes, to confirm what Malaspina said... all versions of the NavOS update disc from the very old V22 (8/2003) to the latest V31 all include the most recent NavOS update for the MKIII, which is 3-1/63.

See this page for a chart.

So don't waste your time trying to get V31 to work - it won't matter anyway! Just use one of the older discs that already comes in Mode 2 - it will get your MKIII up to date just fine.