MinT - Best Known (44, 44+51, s)-Nets in Base 16

Best Known (44, 44+51, s)-Nets in Base 16

Digital (44, 95, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 95, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

Digital (44, 95, 241)-net over F₁₆, using

(44, 95, 257)-net in base 16, using

1 times m-reduction [i] based on (44, 96, 257)-net in base 16, using
- base change [i] based on digital (12, 64, 257)-net over F₆₄, using
  - net from sequence [i] based on digital (12, 256)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
      - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

There is no (44, 95, 22844)-net in base 16, because

1 times m-reduction [i] would yield (44, 94, 22844)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 153968 610985 860153 537853 459152 120103 841860 962565 467474 248473 023850 185135 532814 871604 454642 758292 343699 182806 610251 > 16⁹⁴ [i]