**Core Concept**
The first web space of the foot is a critical area for sensation and movement, and its innervation is primarily provided by a specific nerve. The **deep peroneal nerve** is responsible for the sensory innervation of this area. This nerve is a branch of the **common peroneal nerve**, which itself is a branch of the **sciatic nerve**.

**Why the Correct Answer is Right**
The correct answer is related to the nerve that supplies the first web space. The **deep peroneal nerve** provides sensation to the first web space of the foot, which is the area between the first and second toes. This nerve runs along the anterior aspect of the leg and foot, providing motor innervation to the muscles of the anterior compartment and sensory innervation to the first web space.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not specifically relate to the nerve supplying the first web space.
**Option B:** This option is also incorrect as it is not the primary nerve responsible for the sensory innervation of the first web space.
**Option C:** Similarly, this option does not accurately describe the nerve supply to the first web space.
**Option D:** This option is incorrect because, although it might be related to foot innervation, it is not the correct nerve for the first web space.

**Clinical Pearl / High-Yield Fact**
It's crucial to remember that the **deep peroneal nerve** is responsible for the sensation in the first web space, as damage to this nerve can lead to sensory loss in this area. This knowledge is essential for diagnosing and managing conditions affecting the foot.

**Correct Answer:** Correct Answer: D. Deep peroneal nerve.