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eLabFTW
:notebook: eLabFTW is the most popular open source electronic lab notebook for research labs.
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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
If you absolutely must use an online format, why not encourage your research advisor to check out existing electronic lab notebook stuff? One system, which would contain everyone's work and make it permanently accessible to your advisor, could be very attractive. There are low-cost options available also, like self-hosting eLabFTW.
NOTE:
The number of mentions on this list indicates mentions on common posts plus user suggested alternatives.
Hence, a higher number means a more popular project.