MinT - Best Known (28, 48, s)-Nets in Base 16

Best Known (28, 48, s)-Nets in Base 16

Digital (28, 48, 522)-net over F₁₆, using

trace code for nets [i] based on digital (4, 24, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

Digital (28, 48, 665)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁴⁸, 665, F₁₆, 20) (dual of [665, 617, 21]-code), using
- 19 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 0, 0, 0, 1, 14 times 0) [i] based on linear OA(16⁴⁴, 642, F₁₆, 20) (dual of [642, 598, 21]-code), using
  - trace code [i] based on linear OA(256²², 321, F₂₅₆, 20) (dual of [321, 299, 21]-code), using
    - extended algebraic-geometric code AG_e(F,300P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

There is no (28, 48, 181823)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6277 130466 174162 118079 303678 677558 966173 560026 504875 480451 > 16⁴⁸ [i]