MinT - Best Known (43, 92, s)-Nets in Base 16

Best Known (43, 92, s)-Nets in Base 16

Digital (43, 92, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 92, 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 (43, 92, 244)-net over F₁₆, using

(43, 92, 257)-net in base 16, using

1 times m-reduction [i] based on (43, 93, 257)-net in base 16, using
- base change [i] based on digital (12, 62, 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 (43, 92, 24025)-net in base 16, because

1 times m-reduction [i] would yield (43, 91, 24025)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 37 591275 503517 788956 704016 103385 055065 028186 877818 019135 793625 084578 191109 804947 339720 006618 744626 339392 331501 > 16⁹¹ [i]