I did find 222,278 grids with MCN = 16 (and there are probably more, see below for more details).

Here are a few from band 32, if someone could confirm these I'd be grateful:

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`16: 123456789457189236689237145214573698376918452598624371731892564842365917965741823`

16: 123456789457189236689237145214573698376918452598624371731892564842765913965341827

16: 123456789457189236689237145214573698376918452598624371731892564845361927962745813

16: 123456789457189236689237145214573698376918452598624371731892564845761923962345817

16: 123456789457189236689237145214573698376918452598624371731892564862345917945761823

16: 123456789457189236689237145214573698376918452598624371731892564862745913945361827

The methodology was basically this:

- for each grid compute MCN4 = max clique size using only UA4's

- if an MCN = 17 exists, it would need MCN4 > 10, since 10 UA4's + 7 UA6's can't be mutually disjoint. Further, an initial scan that calculated just MCN4 was done, and this revealed that there is no grid with MCN4 > 13. So the feasible combinations for the hypothetical MCN=17 are limited to (11+6), (12+5), (13+4)

- the grids with MCN4 > 10 were then checked (see table below for the grid counts involved), and a full MCN calculation performed on each, and this found that 222,278 of those grids had MCN = 16, but none had MCN = 17

The ED grid counts by MCN4:

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`11 31,610,628`

12 2,044,701

13 18,432

----------------------

33,673,761

Now perhaps somebody has already done this (!), but I haven't actually come across a definitive statement about the impossibility of an MCN = 17 grid.

And how complete is my MCN=16 grid count? Well, obviously I need to look at the much larger pools of grids with MCN4 = 8, 9, and 10 (the only applicable cases) to do that, and that is my next task. I will do some sampling meanwhile to get an estimate of how many there might be.

Cheers

MM