For n=24 we have 300 balls touching the central ball in our Naïve construction in oblique coördinates. Cribbing from other work describing the Leech lattice we find 196560 balls, including the 300, including for instance (1/10)(−9², 1²²) and its 23∙24/2 relatives in our oblique coördinates.

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2*2*(-9)(-9) + 22*2*1*1 + 2*(23+22)*1*(-9)*1 + (484-20)*1*1*1 = (+ (* 2 2 81) (* 22 2) (* 2 45 -9) 464) =22