Interesting discussion!
Yes, it would be clever to locate a source on the repeating 'N'x periods. The inverse 'iN' following the Barker code is likewise clever.
In terms of an 89 prime, I would like to pipe up on behalf of, the builder --especially a builder who may not have tried this before. My first attempt was with a 5.1cm well (2") and height of 135cm (53"). Working with 2.5mm plywood strips (which are bendy) is really tough, as is cutting them straight, even with a table saw.
I have gone to the 93.5cm (3') square frame as a general ok not too big and not too small size. It's also nice that with 4.25cm well-segments, 2 11N's fit, and with a spacer a 23N fits, and you can also do 3 N7s (with a 1cm filler on each side).
I feel the frame size is non-trivial in realworld build it in your backroom life. Once you have an approximate size (and I am happy to expand or shrink a couple of wells, or even go half-size), then it must be remembered that zero well placement comes into play when moving across the frames. Which is why an 89 prime is likely quite difficult, unless you can make various odd frame sizes.
The next point -- I'm not so willing to sacrifice the LF Hz -- which is where I started: I was really impressed with the LF performance of the N7 (read my first post). It's been quite a journey from (2 days?) ago, but I remain concerned to build as wide a bandwidth QRD as reasonable for the room.
I feel the 23N + 11N is very workable. I'm considering the 17N suggestion, but in terms of frame size and overall length it's not ideal (too short on both counts).
Another perhaps small point is that if one is able to arrange zero wells across the frames you are actually getting 100% QRD across the entire array. Surely this must is a good thing, rather than having your array periods broken up by framing which can be 3-5cm (of nothing).
A last point for me concerns the room itself. The array I'm planning passes opposite a 45 deg. wall which is narrowing the room and then into a drum nook, which is about 1meter shallower than the rest of the room. This must skew all the theory to some not very accountable (by me) extent.
Again, for the builder, a modular technique has many advantages. My 93.5cm frames sit on top of 93.5cm absorbers, and on top of the vertical diffusor will be 93.5cm horizontal diffusion. (Also half-frames remain modular, you just need 2.) And if I want to move these frames, mix and match, it's all easy -- to stack, to get through the door, even to store. I doubt this will happen -- (but I always say that) ...
So I think a reasonable size frame and modular construction, with the rest of the treatment considered, is just as worthwhile a pre-production step as overall dimension.

(is this a rant?)
I come back to the original goal -- to build the best possible diffusion into the room, given certain dimensional and construction constraints. Collo's last suggestion is the 17N, which I'm still considering... though the N23 has some real advantages of its own. Also just to mention, I am thinking of Heimholtz corners with absorption (
John Sayers style, claimed 150Hz-500Hz spec.) -- this works well with an effective diffusion LF of 581Hz:N21 and 405Hz:N11).
In terms of the same repeating N-periods, how about all N11s, (there would be 8). You gain quite a bit of LF over the N17, right? With inverse N11s following the Barker code (or)?
Collo, what do you think of this idea, especially in comparison to all N17?
