SummaryAlgebraic curves are used in many different areas, including error-correcting codes. In such applications, it is important that the algebraic curve C meets some requirements. The curve must be defined over a finite field F q with q elements, and then the curve also should have many points over this field. There are limits on how many points N (C) an algebraic curve C defined over a finite field can have.

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In this paper, we investigate examples of good and optimal Drinfeld modular towers of function fields. Surprisingly, the optimality of these towers has not been investigated in full detail in the literature. We also give an algorithmic approach for obtaining explicit defining equations for some of these towers and, in particular, give a new explicit example of an optimal tower over a quadratic finite field.

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