An overclocker known as Hocayu has set a new world record for DDR4 memory clock speeds. According to HWBOT, a home for overclocking competitions, Hocayu squeezed an effective 5,566MHz out of a G.Skill Trident Z RGB memory kit, along with some serious backup.
Hocayu set the record using a G.Skill Trident Z RGB memory kit paired with an Intel Core i7-8700K on an Asus ROG Maximus XI GENE motherboard. You can pick up most of those components yourself--it's not exactly hard to find a two-generations-old Intel processor or G.Skill memory--but the motherboard will prove a bit tricky because Asus has yet to reveal when it will release the ROG Maximus XI GENE.
Like many overclockers, Hocayu cooled both the memory kit and CPU with liquid nitrogen. Hocayu set the G.Skill memory kit's CL timings at CL24.0 31-31-63 3T for this experiment. In terms of the kit the overclocker used, HWbot lists the Trident Z RGB as being an 8,192MB DDR4 SDRAM. The HWBOT page links to a DDR4-3200 kit on Amazon, but that could just be a default landing page. G.Skill released a kit clocked at 4,600MHz, but it's marked as discontinued, and the 4,700MHz kit it announced in February doesn't appear on its website.
You can check out the CPU configuration used in Hocayu's record-breaking attempt to push DDR4 to its limit via this screenshot: