What exact model are you using?

I have a 16GB GPU as well, but have never run a local model so far. According to the table in the article, 9B and 8-bit -> 13 GB and 27B and 3-bit seem to fit inside the memory. Or is there more space required for context etc?

It depends on the task, but you generally want some context. These models can do things like OCR and summarize a pdf for you, which takes a bit of working memory. Even more so for coding CLIs like opencode-ai, qwen code and mistral ai.

Inference engines like llama.cpp will offload model and context to system ram for you, at the cost of performance. A MoE like 35B-A3B might serve you better than the ones mentioned, even if it doesn't fit entirely on the GPU. I suggest testing all three. Perhaps even 122-A10B if you have plenty of system ram.

Q4 is a common baseline for simple tasks on local models. I like to step up to Q5/Q6 for anything involving tool use on the smallish models I can run (9B and 35B-A3B).

Larger models tolerate lower quants better than small ones, 27B might be usable at 3 bpw where 9B or 4B wouldn't. You can also quantize the context. On llama.cpp you'd set the flags -fa on, -ctk x and ctv y. -h to see valid parameters. K is more sensitive to quantization than V, don't bother lowering it past q8_0. KV quantization is allegedly broken for Qwen 3.5 right now, but I can't tell.