MinT - Best Known (29, 49, s)-Nets in Base 16

Best Known (29, 49, s)-Nets in Base 16

Digital (29, 49, 522)-net over F₁₆, using

1 times m-reduction [i] based on digital (29, 50, 522)-net over F₁₆, using
- trace code for nets [i] based on digital (4, 25, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

Digital (29, 49, 709)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁴⁹, 709, F₁₆, 20) (dual of [709, 660, 21]-code), using
- 62 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 0, 0, 0, 1, 14 times 0, 1, 42 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 (29, 49, 239919)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 100436 023000 829894 770894 417616 930564 526463 934887 938503 174101 > 16⁴⁹ [i]