MinT - Best Known (47, 103, s)-Nets in Base 16

Best Known (47, 103, s)-Nets in Base 16

Digital (47, 103, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 103, 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 (47, 103, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 103, 243)-net over F₁₆, using
- net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
    - a curve from the manYPoints database [i]

(47, 103, 257)-net in base 16, using

2 times m-reduction [i] based on (47, 105, 257)-net in base 16, using
- base change [i] based on digital (12, 70, 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 (47, 103, 20232)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10586 002758 816435 613510 296855 523262 097970 173900 568820 569746 413391 332359 889249 051537 920809 831984 561083 386152 461853 812289 109216 > 16¹⁰³ [i]