For perfect fields of characteristic p, any p-algebra of degree p^{ℓm} and exponent p^m has essential p-dimension at least ℓ+1.
The de R ham W itt complex, cohomological kernels and p^m -extensions in characteristic p
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Essential Dimension, Symbol Length and $p$-rank
For perfect fields of characteristic p, any p-algebra of degree p^{ℓm} and exponent p^m has essential p-dimension at least ℓ+1.