MinT - Best Known (49, 49+61, s)-Nets in Base 16

Best Known (49, 49+61, s)-Nets in Base 16

Digital (49, 110, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 110, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(49, 110, 257)-net in base 16, using

1 times m-reduction [i] based on (49, 111, 257)-net in base 16, using
- base change [i] based on digital (12, 74, 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 (49, 110, 19024)-net in base 16, because

1 times m-reduction [i] would yield (49, 109, 19024)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 177592 941364 820144 659471 132160 625907 640673 802471 378375 433110 886068 369879 082065 205352 593444 906750 152117 550351 917712 854321 218189 657676 > 16¹⁰⁹ [i]