The finest socks are knitted by 240 or 276 / 280 needles machines. They can make lightweight, very comfortable and flexible socks with superior fit. Moreover, these machines can process very fine yarn, and they allow to use various small patterns. Knitting machines with 200 needles are good too, and they’re often used by manufacturers of fine socks.
Some brands that offer socks knitted by 240 or 276 needles machines: Bresciani, Brioni, Canali, Fort Belvedere, Gammarelli, Mazarin, Pantherella (rarely), William Abraham.