Data from the Department for Health and Social care shows 6,148 people who tested positive for Covid-19 in Buckinghamshire were transferred to the Test and Trace service between May 28 and November 25.
That means 725 new cases were transferred in the latest seven-day period.
Contact tracers ask new patients to give details for anyone they were in close contact with in the 48 hours before their symptoms started.
This led to 14,621 close contacts being identified over the period – those not managed by local health protection teams, which are dealt with through a call centre or online.
But just 62.5% of those were reached, meaning 5,490 people were not contacted or did not respond
As of November 18, people under the age of 18 who have been in contact with someone who has tested positive for Covid-19 are no longer all being traced individually, according to the latest Test and Trace report.
Instead, a parent or guardian in the household is asked to confirm they have told the child to self-isolate, and if they have done so the child is recorded as having been reached.
If no parental permission is provided, the usual contact-tracing routes are followed.
This change means it is no longer possible to compare historically the proportion of contacts that have been reached each week under Test and Trace.
Across England, 71.3% of contacts not managed by local health protection teams were reached and told to self-isolate by NHS Test and Trace in the latest week to November 25.
Local health protection teams deal with cases linked to settings such as hospitals, schools and prisons.
The contact tracing rate including these cases was 72.5%, according to the new calculations. Under the previous calculations, 60.5% of close contacts were reached in the week ending November 18.
Around 116,000 new cases were transferred nationally in the week to November 25.