We compute the strong-liar set L (n) of the Miller--Rabin primalitytest for every odd composite n in 9, 10^11 and every witnessa in 2, 1000, recording for each witness the total countₐ = \#\n: \, a L (n) \ and for each composite thesmall-height intersection ₙ = |L (n) 2, 1000|, the statistic relevant to fixed small-witness testing. Monier'sclassical formula is exact for |L (n) | in the full unit group (Z/nZ) ^ but has no resolving power forₙ: for our extreme composites |L (n) | exceeds ₙby six orders of magnitude. The enumeration evaluates approximately4. 58 10^13 Miller--Rabin instances in 4. 62 wall-clockdays on a single 24-core workstation, and is validated againstthe base-2 strong-pseudoprime decade counts46, 488, 1282, 3291, 8607 at N=10^6, 10^8, 10^9, 10^10, 10^11 (OEIS A055552) together with three furtherindependent checks. Three findings emerge. First, the worst fixedwitness in 2, 1000 at every scale is a=256=2⁸, and perfectpowers dominate the witness ranking; a local Chinese RemainderTheorem (CRT) criterion characterising when a=bᵏ is a strong liarsupplies the mechanism, though not a complete prediction of theranking. Second, the worst composites pivot fromPomerance--Selfridge--Wagstaff semiprimes p (2p-1) to 3-primeCarmichael numbers in the extreme tail, with 9 of the top 10 atN 10^10 being Carmichaels. Third, the record-holdern^ = 151 751 28351 with ₍^ = 371remains globally maximal under extension from 10^10 to10^11. We isolate the small-height extremal problem₍ ₍|L (n) 2, A| as the central open question raisedby the data, and prove two structural mechanisms: the local CRTcriterion, and prime-square order halving under a Legendre-symbolnon-residue condition.
John Janik (Fri,) studied this question.