Throughout history, numerous skilled swordsmiths in Japan have been celebrated for their craftsmanship and contribution to the art of samurai sword-making. Determining the "best" samurai sword maker is subjective and can depend on various factors such as individual preferences, historical context, and specific criteria. Here are a few renowned swordsmiths who are highly regarded for their skill:

1. Masamune: Goro Nyudo Masamune, commonly known as Masamune, is considered one of the greatest swordsmiths in Japanese history. Active during the Kamakura period (1185-1333), he is renowned for his exceptional skill in forging swords that embody superior craftsmanship, exquisite aesthetics, and outstanding cutting performance.
2. Muramasa: Sengo Muramasa, an illustrious swordsmith from the Muromachi period (1336-1573), is renowned for his distinctive style characterized by sharpness and aggression. Muramasa blades were known for their cutting ability, though they were also believed to have a curse, as legends portrayed them as "bloodthirsty" swords.
3. Bizen School: The Bizen school of swordsmiths, active during various periods from the Heian (794-1185) to the Muromachi (1336-1573), produced swords of exceptional quality. The Bizen tradition, known for its distinctive hamon (temper line) and unique steel characteristics, was highly regarded and influential in shaping the development of Japanese swords.
4. Yamato School: The Yamato school, based in Yamato Province (present-day Nara Prefecture), produced swords characterized by elegant and graceful designs. Active during the Heian and Kamakura periods, swordsmiths of the Yamato school were known for their artistic approach, skillful execution, and ability to produce swords with outstanding balance and quality.
5. Osafune School: The Osafune school, centered in the Osafune region of Bizen Province, thrived during the Kamakura and Muromachi periods. Swordsmiths from this school were recognized for their skill in forging swords with excellent balance, durability, and refined artistic elements.

It is essential to note that the quality of a sword is not solely determined by the swordsmith but also influenced by factors such as the specific sword's condition, age, and individual preferences. The reputation and recognition of swordsmiths can vary over time and among different experts. Ultimately, the "best" samurai sword maker is subjective and can vary depending on personal opinions, historical context, and the specific criteria being considered.