What's the shortest word that has the most anagrams?

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For three-letter words, use the following formula:

APT, PAT, TAP ARE, EAR, ERA EAT, EAT, ETA, TEA ART, RAT, TAR ART, RAT, TAR ART, RAT, TAR ART, RAT, TAR ART, RAT, TAR ART, RAT, TAR ART,

For four-letter words, use the following formula:

EATS, SATE, SEAT, SETA, TEAS LATE, TALE, TEAL PATE, PEAT, TAPE PARE, PEAR, RAPE, REAP RATE, TARE, TEAR EATS, SATE, SEAT, SETA, TEAS LATE, TALE, TEAL PATE, PEAT, TAPE PARE, PEAR, RAPE, REAP RATE, TARE, TEAR

For six-letter words, use the following formula:

MANTEL, MANTLE, MENTAL, LAMENT, MANTEL, MANTEL, MANTEL, MANTEL, MANTEL,

These should suffice as a good starting point. With the exception of APT/ART, etc., which has an A plus two consonants that can be put next to each other, each of these terms contains an A and an E. Common consonants such as L, R, S, and T also appear frequently.

When playing Boggle, these combinations are vital.