Packing superballs from codes and algebraic curves (Q928222)

Superballs in \(\mathbb{R}^n\) with respect to the \(L_{\sigma}\)-distance \(d(x,y)=\left(\sum (x_i-y_i)^\sigma\right)^{1/\sigma}\) are packed by using codes of good parameters (with respect to the Hamming distance) and algebraic curves with many rational points over finite fields. Numerical results are presented to show that the lower bounds on the best possible packings are improved.