Short answers, pulled from the story.
The Lex Fufia Caninia of 2 BC placed numerical limits on the number of slaves a Roman master could free through a will. The caps were proportional to estate size, ranging from half for smaller estates to a maximum of one hundred freed slaves regardless of total estate size.
The law served several purposes: protecting heirs and creditors from end-of-life generosity that depleted estates, curbing the practice of freeing slaves solely to inflate funeral processions, and reframing manumission from a purely private matter into a state interest. It was part of a broader program of Augustan social legislation alongside the Lex Iunia Norbana and the Lex Aelia Sentia.
Estates of one or two slaves were exempt. Estates of three to ten slaves could free no more than half; over ten to thirty, a third; over thirty to one hundred, a fourth; over one hundred to five hundred, a fifth. A cap of one hundred applied to all estates regardless of size.
The Lex Fufia Caninia was abolished in AD 528 by the emperor Justinian as part of reforms that dismantled most of the Augustan legislation on manumission.
Most scholars in the 21st century do not view the law as primarily aimed at reducing overall manumissions. Because testamentary manumission was thought to be the most common path to citizenship, the numerical caps likely pushed more masters toward informal manumission, which granted freedom but not full citizenship rights.
Every slave designated for freedom had to be listed by name in the will. A description or job title could substitute for a name only if it was unique enough to identify a single individual, such as the unborn child of a specifically named female slave.