what "particular" value does a manufacturer need to exceed ?
Under US certification rules:
14CFR 23.233 (Normal category)
(a) A 90 degree cross-component of wind velocity, demonstrated to be safe for taxiing, takeoff, and landing must be established and must be not less than 0.2 Vs0.
14CFR 25.237 (Transport Category)
(a) For landplanes and amphibians, a 90-degree cross component of wind velocity, demonstrated to be safe for takeoff and landing, must be established for dry runways and must be at least 20 knots or 0.2 Vsr0, whichever is greater, except that it need not exceed 25 knots.
Strangely, 23.1585(2) requires the "maximum demonstrated values of crosswind for takeoff and landing" to be recorded in the flight manual. I cannot find a corresponding entry for transport category aircraft.
Some manufacturers (Mooney, for example) choose to record exactly 0.2 Vs0 and accompany the AFM entry with an annotation that makes perfectly clear that the value is not to be considered limiting.
(and I'm sorry if my previous post was somewhat sharper than necessary)