The strict answer to your question is in Gerzon's

"The Design of Precisely Coincident Microphone Arrays for Stereo and 
Surround Sound"

http://www.aes.org/e-lib/browse.cfm?elib=2466

There's a corrected copy at 
https://groups.yahoo.com/neo/groups/SoundfieldMic/files/Ricardo/.  You 
might have to join.

I used to be able to translate da maths to practical stuff but this 
Millenium my single remaining brain cell has given up.

Aaron Heller & Fons Adrieansen are your best bets.

You need to know the polar directivity patterns of your 16 microphones and 
their 'exact' postion.

Bet yus guys didn't know that paper was about more than Tetrahedral mikes 
:)

It's just that in da old days, the computing power required was thought 
impossible eg "the impossible task of 'tweaking' 16 complex (in both 
senses) frequency responses to get the (unknown) best match to the desired 
polar diagrams."

Today, computing power is (usually) never a constraint and the much greater 
problem is knowing how to use it.

> I am wondering how I go about converting a recording made with a 16 
microphone array into B format?
...
> The recordings were made using a "microphone array of 16 microphones 
arranged in 4 staggered rows, spaced such there is a 5 cm distance form 
each microphone to its immediate neighbors. The array is in a plane which 
in all recordings is parallel to the ground."

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